LMFDB - Embedded newform 980.2.x.m.863.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [980,2,Mod(67,980)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(980, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("980.67"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.x (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [72,2,0,0,8,16,0,-4,0,-2,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			863.11
Character	$\chi$	$=$	980.863
Dual form			980.2.x.m.67.11

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.441772 - 1.34344i) q^{2} +(-1.20413 - 0.322645i) q^{3} +(-1.60968 - 1.18699i) q^{4} +(-2.09885 + 0.771256i) q^{5} +(-0.965404 + 1.47514i) q^{6} +(-2.30576 + 1.63813i) q^{8} +(-1.25225 - 0.722989i) q^{9} +(0.108927 + 3.16040i) q^{10} +(-0.824629 + 0.476100i) q^{11} +(1.55528 + 1.94864i) q^{12} +(3.15680 + 3.15680i) q^{13} +(2.77612 - 0.251508i) q^{15} +(1.18211 + 3.82134i) q^{16} +(-2.56885 - 0.688322i) q^{17} +(-1.52450 + 1.36293i) q^{18} +(1.99048 - 3.44760i) q^{19} +(4.29394 + 1.24984i) q^{20} +(0.275315 + 1.31817i) q^{22} +(0.141582 + 0.528392i) q^{23} +(3.30496 - 1.22857i) q^{24} +(3.81033 - 3.23750i) q^{25} +(5.63557 - 2.84640i) q^{26} +(3.91905 + 3.91905i) q^{27} +7.23080i q^{29} +(0.888526 - 3.84067i) q^{30} +(3.41863 - 1.97375i) q^{31} +(5.65597 + 0.100058i) q^{32} +(1.14657 - 0.307222i) q^{33} +(-2.05957 + 3.14702i) q^{34} +(1.15754 + 2.65019i) q^{36} +(0.269180 + 1.00460i) q^{37} +(-3.75232 - 4.19714i) q^{38} +(-2.78267 - 4.81972i) q^{39} +(3.57603 - 5.21652i) q^{40} -3.71449 q^{41} +(8.73324 - 8.73324i) q^{43} +(1.89251 + 0.212459i) q^{44} +(3.18590 + 0.551635i) q^{45} +(0.772411 + 0.0432210i) q^{46} +(3.09794 - 0.830089i) q^{47} +(-0.190479 - 4.98278i) q^{48} +(-2.66610 - 6.54919i) q^{50} +(2.87114 + 1.65765i) q^{51} +(-1.33434 - 8.82853i) q^{52} +(-0.760768 + 2.83923i) q^{53} +(6.99635 - 3.53369i) q^{54} +(1.36358 - 1.63526i) q^{55} +(-3.50914 + 3.50914i) q^{57} +(9.71416 + 3.19436i) q^{58} +(6.30084 + 10.9134i) q^{59} +(-4.76720 - 2.89038i) q^{60} +(-3.01183 + 5.21665i) q^{61} +(-1.14136 - 5.46468i) q^{62} +(2.63307 - 7.55427i) q^{64} +(-9.06036 - 4.19095i) q^{65} +(0.0937861 - 1.67607i) q^{66} +(3.85605 - 14.3910i) q^{67} +(3.31799 + 4.15717i) q^{68} -0.681932i q^{69} +7.60710i q^{71} +(4.07174 - 0.384313i) q^{72} +(-3.80964 + 14.2178i) q^{73} +(1.46853 + 0.0821731i) q^{74} +(-5.63268 + 2.66898i) q^{75} +(-7.29629 + 3.18685i) q^{76} +(-7.70432 + 1.60914i) q^{78} +(-5.34864 + 9.26412i) q^{79} +(-5.42830 - 7.10869i) q^{80} +(-1.28561 - 2.22674i) q^{81} +(-1.64096 + 4.99021i) q^{82} +(5.72446 - 5.72446i) q^{83} +(5.92250 - 0.536560i) q^{85} +(-7.87451 - 15.5907i) q^{86} +(2.33298 - 8.70680i) q^{87} +(1.12148 - 2.44862i) q^{88} +(1.83403 + 1.05888i) q^{89} +(2.14853 - 4.03637i) q^{90} +(0.399294 - 1.01860i) q^{92} +(-4.75329 + 1.27364i) q^{93} +(0.253402 - 4.52861i) q^{94} +(-1.51872 + 8.77117i) q^{95} +(-6.77823 - 1.94535i) q^{96} +(3.08588 - 3.08588i) q^{97} +1.37686 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 2 q^{2} + 8 q^{5} + 16 q^{6} - 4 q^{8} - 2 q^{10} - 10 q^{12} - 28 q^{16} - 4 q^{17} - 20 q^{18} + 56 q^{20} - 16 q^{22} - 16 q^{25} + 4 q^{26} - 32 q^{30} - 38 q^{32} + 64 q^{33} + 16 q^{36} - 4 q^{37}+ \cdots + 24 q^{97}+O(q^{100}) $ 72 * q + 2 * q^2 + 8 * q^5 + 16 * q^6 - 4 * q^8 - 2 * q^10 - 10 * q^12 - 28 * q^16 - 4 * q^17 - 20 * q^18 + 56 * q^20 - 16 * q^22 - 16 * q^25 + 4 * q^26 - 32 * q^30 - 38 * q^32 + 64 * q^33 + 16 * q^36 - 4 * q^37 - 12 * q^38 - 2 * q^40 + 40 * q^41 + 12 * q^45 - 28 * q^46 - 12 * q^48 - 28 * q^50 - 48 * q^52 - 24 * q^53 - 16 * q^57 + 30 * q^58 - 10 * q^60 + 20 * q^61 - 56 * q^62 + 4 * q^65 - 44 * q^66 + 12 * q^68 + 44 * q^72 + 12 * q^73 - 112 * q^76 + 64 * q^78 - 52 * q^80 - 52 * q^81 + 34 * q^82 + 16 * q^85 + 64 * q^86 + 16 * q^88 + 32 * q^90 + 44 * q^92 + 12 * q^93 + 48 * q^96 + 24 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.441772	−	1.34344i	0.312380	−	0.949957i
$2$	0.441772	−	1.34344i	0.312380	−	0.949957i
$3$	−1.20413	−	0.322645i	−0.695203	−	0.186279i	−0.106122	−	0.994353i	$-0.533843\pi$
$3$	−1.20413	−	0.322645i	−0.695203	−	0.186279i	−0.589081	+	0.808074i	$0.700510\pi$
$4$	−1.60968	−	1.18699i	−0.804838	−	0.593495i
$5$	−2.09885	+	0.771256i	−0.938633	+	0.344916i
$5$	−2.09885	+	0.771256i	−0.938633	+	0.344916i
$6$	−0.965404	+	1.47514i	−0.394125	+	0.602224i
$7$		0			0
$7$		0			0
$8$	−2.30576	+	1.63813i	−0.815210	+	0.579166i
$9$	−1.25225	−	0.722989i	−0.417418	−	0.240996i
$10$	0.108927	+	3.16040i	0.0344457	+	0.999407i
$11$	−0.824629	+	0.476100i	−0.248635	+	0.143549i	−0.619139	−	0.785281i	$-0.712518\pi$
$11$	−0.824629	+	0.476100i	−0.248635	+	0.143549i	0.370504	+	0.928831i	$0.379185\pi$
$12$	1.55528	+	1.94864i	0.448970	+	0.562524i
$13$	3.15680	+	3.15680i	0.875540	+	0.875540i	0.993069	−	0.117529i	$-0.0374974\pi$
$13$	3.15680	+	3.15680i	0.875540	+	0.875540i	−0.117529	+	0.993069i	$0.537497\pi$
$14$		0			0
$15$	2.77612	−	0.251508i	0.716792	−	0.0649391i
$16$	1.18211	+	3.82134i	0.295528	+	0.955334i
$17$	−2.56885	−	0.688322i	−0.623038	−	0.166943i	−0.0665295	−	0.997784i	$-0.521193\pi$
$17$	−2.56885	−	0.688322i	−0.623038	−	0.166943i	−0.556508	+	0.830842i	$0.687859\pi$
$18$	−1.52450	+	1.36293i	−0.359329	+	0.321247i
$19$	1.99048	−	3.44760i	0.456646	−	0.790935i	−0.542135	−	0.840292i	$-0.682384\pi$
$19$	1.99048	−	3.44760i	0.456646	−	0.790935i	0.998781	+	0.0493567i	$0.0157171\pi$
$20$	4.29394	+	1.24984i	0.960154	+	0.279472i
$21$		0			0
$22$	0.275315	+	1.31817i	0.0586973	+	0.281034i
$23$	0.141582	+	0.528392i	0.0295219	+	0.110177i	0.979115	−	0.203309i	$-0.0651696\pi$
$23$	0.141582	+	0.528392i	0.0295219	+	0.110177i	−0.949593	+	0.313486i	$0.898503\pi$
$24$	3.30496	−	1.22857i	0.674623	−	0.250782i
$25$	3.81033	−	3.23750i	0.762066	−	0.647500i
$26$	5.63557	−	2.84640i	1.10523	−	0.558225i
$27$	3.91905	+	3.91905i	0.754222	+	0.754222i
$28$		0			0
$29$			7.23080i			1.34273i	0.741129	+	0.671363i	$0.234291\pi$
$29$			7.23080i			1.34273i	−0.741129	+	0.671363i	$0.765709\pi$
$30$	0.888526	−	3.84067i	0.162222	−	0.701207i
$31$	3.41863	−	1.97375i	0.614004	−	0.354495i	−0.160527	−	0.987031i	$-0.551319\pi$
$31$	3.41863	−	1.97375i	0.614004	−	0.354495i	0.774531	+	0.632536i	$0.217986\pi$
$32$	5.65597	+	0.100058i	0.999844	+	0.0176879i
$33$	1.14657	−	0.307222i	0.199592	−	0.0534805i
$34$	−2.05957	+	3.14702i	−0.353213	+	0.539710i
$35$		0			0
$36$	1.15754	+	2.65019i	0.192924	+	0.441698i
$37$	0.269180	+	1.00460i	0.0442530	+	0.165154i	0.984516	−	0.175294i	$-0.0560877\pi$
$37$	0.269180	+	1.00460i	0.0442530	+	0.165154i	−0.940263	+	0.340449i	$0.889421\pi$
$38$	−3.75232	−	4.19714i	−0.608707	−	0.680867i
$39$	−2.78267	−	4.81972i	−0.445584	−	0.771773i
$40$	3.57603	−	5.21652i	0.565419	−	0.824804i
$41$	−3.71449			−0.580106			−0.290053	−	0.957011i	$-0.593673\pi$
$41$	−3.71449			−0.580106			−0.290053	+	0.957011i	$0.593673\pi$
$42$		0			0
$43$	8.73324	−	8.73324i	1.33181	−	1.33181i	0.428052	−	0.903754i	$-0.359200\pi$
$43$	8.73324	−	8.73324i	1.33181	−	1.33181i	0.903754	−	0.428052i	$-0.140800\pi$
$44$	1.89251	+	0.212459i	0.285307	+	0.0320295i
$45$	3.18590	+	0.551635i	0.474926	+	0.0822329i
$46$	0.772411	+	0.0432210i	0.113886	+	0.00637258i
$47$	3.09794	−	0.830089i	0.451880	−	0.121081i	−0.0256988	−	0.999670i	$-0.508181\pi$
$47$	3.09794	−	0.830089i	0.451880	−	0.121081i	0.477579	+	0.878589i	$0.341514\pi$
$48$	−0.190479	−	4.98278i	−0.0274933	−	0.719202i
$49$		0			0
$50$	−2.66610	−	6.54919i	−0.377044	−	0.926196i
$51$	2.87114	+	1.65765i	0.402040	+	0.232118i
$52$	−1.33434	−	8.82853i	−0.185039	−	1.22430i
$53$	−0.760768	+	2.83923i	−0.104500	+	0.389998i	−0.998288	−	0.0584914i	$-0.981371\pi$
$53$	−0.760768	+	2.83923i	−0.104500	+	0.389998i	0.893788	+	0.448489i	$0.148038\pi$
$54$	6.99635	−	3.53369i	0.952082	−	0.480875i
$55$	1.36358	−	1.63526i	0.183864	−	0.220498i
$56$		0			0
$57$	−3.50914	+	3.50914i	−0.464797	+	0.464797i
$58$	9.71416	+	3.19436i	1.27553	+	0.419440i
$59$	6.30084	+	10.9134i	0.820300	+	1.42080i	0.905459	+	0.424433i	$0.139527\pi$
$59$	6.30084	+	10.9134i	0.820300	+	1.42080i	−0.0851594	+	0.996367i	$0.527140\pi$
$60$	−4.76720	−	2.89038i	−0.615442	−	0.373147i
$61$	−3.01183	+	5.21665i	−0.385626	+	0.667923i	−0.991856	−	0.127366i	$-0.959348\pi$
$61$	−3.01183	+	5.21665i	−0.385626	+	0.667923i	0.606230	+	0.795289i	$0.292681\pi$
$62$	−1.14136	−	5.46468i	−0.144953	−	0.694015i
$63$		0			0
$64$	2.63307	−	7.55427i	0.329134	−	0.944283i
$65$	−9.06036	−	4.19095i	−1.12380	−	0.519823i
$66$	0.0937861	−	1.67607i	0.0115443	−	0.206310i
$67$	3.85605	−	14.3910i	0.471092	−	1.75814i	−0.164766	−	0.986333i	$-0.552687\pi$
$67$	3.85605	−	14.3910i	0.471092	−	1.75814i	0.635858	−	0.771806i	$-0.280647\pi$
$68$	3.31799	+	4.15717i	0.402365	+	0.504131i
$69$		−	0.681932i		−	0.0820949i
$70$		0			0
$71$			7.60710i			0.902797i	0.892322	+	0.451399i	$0.149075\pi$
$71$			7.60710i			0.902797i	−0.892322	+	0.451399i	$0.850925\pi$
$72$	4.07174	−	0.384313i	0.479860	−	0.0452917i
$73$	−3.80964	+	14.2178i	−0.445885	+	1.66406i	0.267705	+	0.963501i	$0.413735\pi$
$73$	−3.80964	+	14.2178i	−0.445885	+	1.66406i	−0.713590	+	0.700564i	$0.752932\pi$
$74$	1.46853	+	0.0821731i	0.170713	+	0.00955243i
$75$	−5.63268	+	2.66898i	−0.650406	+	0.308187i
$76$	−7.29629	+	3.18685i	−0.836942	+	0.365557i
$77$		0			0
$78$	−7.70432	+	1.60914i	−0.872343	+	0.182199i
$79$	−5.34864	+	9.26412i	−0.601769	+	1.04230i	0.390784	+	0.920483i	$0.372204\pi$
$79$	−5.34864	+	9.26412i	−0.601769	+	1.04230i	−0.992553	+	0.121813i	$0.961129\pi$
$80$	−5.42830	−	7.10869i	−0.606903	−	0.794776i
$81$	−1.28561	−	2.22674i	−0.142846	−	0.247416i
$82$	−1.64096	+	4.99021i	−0.181213	+	0.551076i
$83$	5.72446	−	5.72446i	0.628341	−	0.628341i	−0.319309	−	0.947651i	$-0.603451\pi$
$83$	5.72446	−	5.72446i	0.628341	−	0.628341i	0.947651	+	0.319309i	$0.103451\pi$
$84$		0			0
$85$	5.92250	−	0.536560i	0.642386	−	0.0581981i
$86$	−7.87451	−	15.5907i	−0.849130	−	1.68119i
$87$	2.33298	−	8.70680i	0.250122	−	0.933467i
$88$	1.12148	−	2.44862i	0.119551	−	0.261024i
$89$	1.83403	+	1.05888i	0.194407	+	0.112241i	0.594044	−	0.804433i	$-0.297531\pi$
$89$	1.83403	+	1.05888i	0.194407	+	0.112241i	−0.399637	+	0.916673i	$0.630864\pi$
$90$	2.14853	−	4.03637i	0.226475	−	0.425471i
$91$		0			0
$92$	0.399294	−	1.01860i	0.0416293	−	0.106196i
$93$	−4.75329	+	1.27364i	−0.492893	+	0.132070i
$94$	0.253402	−	4.52861i	0.0261365	−	0.467090i
$95$	−1.51872	+	8.77117i	−0.155817	+	0.899903i
$96$	−6.77823	−	1.94535i	−0.691800	−	0.198547i
$97$	3.08588	−	3.08588i	0.313324	−	0.313324i	−0.532872	−	0.846196i	$-0.678887\pi$
$97$	3.08588	−	3.08588i	0.313324	−	0.313324i	0.846196	+	0.532872i	$0.178887\pi$
$98$		0			0
$99$	1.37686			0.138379
$100$	−9.97627	+	0.688506i	−0.997627	+	0.0688506i
$101$	−0.715074	−	1.23854i	−0.0711525	−	0.123240i	0.828254	−	0.560353i	$-0.189334\pi$
$101$	−0.715074	−	1.23854i	−0.0711525	−	0.123240i	−0.899407	+	0.437113i	$0.856001\pi$
$102$	3.49535	−	3.12491i	0.346091	−	0.309412i
$103$	2.63366	+	9.82894i	0.259502	+	0.968474i	0.965530	+	0.260291i	$0.0838184\pi$
$103$	2.63366	+	9.82894i	0.259502	+	0.968474i	−0.706028	+	0.708183i	$0.749515\pi$
$104$	−12.4501	−	2.10758i	−1.22083	−	0.206666i
$105$		0			0
$106$	3.47825	+	2.27634i	0.337838	+	0.221097i
$107$	0.0388547	−	0.0104111i	0.00375622	−	0.00100648i	−0.256940	−	0.966427i	$-0.582714\pi$
$107$	0.0388547	−	0.0104111i	0.00375622	−	0.00100648i	0.260697	+	0.965421i	$0.416048\pi$
$108$	−1.65653	−	10.9603i	−0.159400	−	1.05465i
$109$	5.44983	−	3.14646i	0.521999	−	0.301376i	−0.215753	−	0.976448i	$-0.569221\pi$
$109$	5.44983	−	3.14646i	0.521999	−	0.301376i	0.737752	+	0.675072i	$0.235887\pi$
$110$	−1.59449	−	2.55430i	−0.152029	−	0.243543i
$111$		−	1.29651i		−	0.123059i
$112$		0			0
$113$	10.8513	+	10.8513i	1.02081	+	1.02081i	0.999779	+	0.0210265i	$0.00669344\pi$
$113$	10.8513	+	10.8513i	1.02081	+	1.02081i	0.0210265	+	0.999779i	$0.493307\pi$
$114$	3.16409	+	6.26456i	0.296344	+	0.586730i
$115$	−0.704685	−	0.999818i	−0.0657122	−	0.0932335i
$116$	8.58288	−	11.6392i	0.796900	−	1.08068i
$117$	−1.67078	−	6.23545i	−0.154464	−	0.576468i
$118$	17.4450	−	3.64360i	1.60595	−	0.335420i
$119$		0			0
$120$	−5.98907	+	5.12756i	−0.546725	+	0.468080i
$121$	−5.04666	+	8.74107i	−0.458787	+	0.794643i
$122$	5.67772	+	6.35079i	0.514037	+	0.574974i
$123$	4.47272	+	1.19846i	0.403292	+	0.108062i
$124$	−7.84570	−	0.880785i	−0.704565	−	0.0790968i
$125$	−5.50036	+	9.73376i	−0.491967	+	0.870614i
$126$		0			0
$127$	1.22418	+	1.22418i	0.108629	+	0.108629i	0.759332	−	0.650703i	$-0.225526\pi$
$127$	1.22418	+	1.22418i	0.108629	+	0.108629i	−0.650703	+	0.759332i	$0.725526\pi$
$128$	−8.98551	−	6.87464i	−0.794214	−	0.607638i
$129$	−13.3337	+	7.69820i	−1.17396	+	0.677788i
$130$	−9.63291	+	10.3206i	−0.844862	+	0.905179i
$131$	−1.12982	−	0.652300i	−0.0987126	−	0.0569918i	0.449831	−	0.893114i	$-0.351484\pi$
$131$	−1.12982	−	0.652300i	−0.0987126	−	0.0569918i	−0.548544	+	0.836122i	$0.684818\pi$
$132$	−2.21027	−	0.866437i	−0.192380	−	0.0754137i
$133$		0			0
$134$	−17.6300	−	11.5379i	−1.52300	−	0.996724i
$135$	−11.2481	−	5.20290i	−0.968081	−	0.447794i
$136$	7.05072	−	2.62100i	0.604594	−	0.224749i
$137$	−1.12037	−	0.300203i	−0.0957198	−	0.0256480i	0.210641	−	0.977563i	$-0.432445\pi$
$137$	−1.12037	−	0.300203i	−0.0957198	−	0.0256480i	−0.306361	+	0.951915i	$0.599111\pi$
$138$	−0.916136	−	0.301258i	−0.0779867	−	0.0256448i
$139$	−17.4513			−1.48020			−0.740099	−	0.672498i	$-0.765221\pi$
$139$	−17.4513			−1.48020			−0.740099	+	0.672498i	$0.765221\pi$
$140$		0			0
$141$	−3.99813			−0.336704
$142$	10.2197	+	3.36060i	0.857619	+	0.282015i
$143$	−4.10614	−	1.10024i	−0.343373	−	0.0920065i
$144$	1.28248	−	5.63993i	0.106873	−	0.469994i
$145$	−5.57680	−	15.1763i	−0.463128	−	1.26033i
$146$	17.4178	+	11.3990i	1.44151	+	0.943392i
$147$		0			0
$148$	0.759151	−	1.93659i	0.0624018	−	0.159186i
$149$	9.70894	+	5.60546i	0.795387	+	0.459217i	0.841856	−	0.539703i	$-0.181463\pi$
$149$	9.70894	+	5.60546i	0.795387	+	0.459217i	−0.0464684	+	0.998920i	$0.514797\pi$
$150$	1.09726	+	8.74627i	0.0895910	+	0.714130i
$151$	−13.0081	+	7.51022i	−1.05858	+	0.611173i	−0.925040	−	0.379870i	$-0.875969\pi$
$151$	−13.0081	+	7.51022i	−1.05858	+	0.611173i	−0.133543	+	0.991043i	$0.542635\pi$
$152$	1.05806	+	11.2100i	0.0858200	+	0.909252i
$153$	2.71920	+	2.71920i	0.219835	+	0.219835i
$154$		0			0
$155$	−5.65292	+	6.77924i	−0.454054	+	0.544521i
$156$	−1.24177	+	11.0612i	−0.0994209	+	0.885604i
$157$	7.27171	+	1.94845i	0.580345	+	0.155503i	0.537037	−	0.843559i	$-0.319544\pi$
$157$	7.27171	+	1.94845i	0.580345	+	0.155503i	0.0433084	+	0.999062i	$0.486210\pi$
$158$	10.0829	+	11.2782i	0.802155	+	0.897247i
$159$	1.83212	−	3.17333i	0.145297	−	0.251662i
$160$	−11.9482	+	4.15220i	−0.944587	+	0.328260i
$161$		0			0
$162$	−3.55944	+	0.743432i	−0.279656	+	0.0584095i
$163$	1.72089	+	6.42243i	0.134790	+	0.503044i	0.999999	+	0.00163153i	$0.000519334\pi$
$163$	1.72089	+	6.42243i	0.134790	+	0.503044i	−0.865208	+	0.501412i	$0.832814\pi$
$164$	5.97913	+	4.40906i	0.466891	+	0.344290i
$165$	−2.16953	+	1.52911i	−0.168897	+	0.119041i
$166$	−5.16158	−	10.2194i	−0.400616	−	0.793179i
$167$	−5.93258	−	5.93258i	−0.459077	−	0.459077i	0.439276	−	0.898352i	$-0.355235\pi$
$167$	−5.93258	−	5.93258i	−0.459077	−	0.459077i	−0.898352	+	0.439276i	$0.855235\pi$
$168$		0			0
$169$			6.93083i			0.533141i
$170$	1.89556	−	8.19358i	0.145382	−	0.628419i
$171$	−4.98516	+	2.87818i	−0.381225	+	0.220100i
$172$	−24.4239	+	3.69142i	−1.86231	+	0.281468i
$173$	−2.13818	+	0.572923i	−0.162563	+	0.0435585i	−0.339182	−	0.940721i	$-0.610150\pi$
$173$	−2.13818	+	0.572923i	−0.162563	+	0.0435585i	0.176620	+	0.984279i	$0.443484\pi$
$174$	−10.6664	−	6.98064i	−0.808621	−	0.529201i
$175$		0			0
$176$	−2.79414	−	2.58838i	−0.210616	−	0.195106i
$177$	−4.06587	−	15.1740i	−0.305610	−	1.14055i
$178$	2.23276	−	1.99613i	0.167353	−	0.149616i
$179$	8.23493	+	14.2633i	0.615507	+	1.06609i	0.990295	+	0.138980i	$0.0443822\pi$
$179$	8.23493	+	14.2633i	0.615507	+	1.06609i	−0.374788	+	0.927111i	$0.622284\pi$
$180$	−4.47348	−	4.66958i	−0.333433	−	0.348050i
$181$	5.97636			0.444219			0.222110	−	0.975022i	$-0.428706\pi$
$181$	5.97636			0.444219			0.222110	+	0.975022i	$0.428706\pi$
$182$		0			0
$183$	5.30976	−	5.30976i	0.392508	−	0.392508i
$184$	−1.19203	−	0.986415i	−0.0878775	−	0.0727195i
$185$	−1.33977	−	1.90089i	−0.0985018	−	0.139756i
$186$	−0.388806	+	6.94843i	−0.0285086	+	0.509483i
$187$	2.44606	−	0.655419i	0.178873	−	0.0479290i
$188$	−5.97198	−	2.34104i	−0.435551	−	0.170738i
$189$		0			0
$190$	11.1126	+	5.91516i	0.806195	+	0.429131i
$191$	6.96830	+	4.02315i	0.504209	+	0.291105i	0.730450	−	0.682966i	$-0.239310\pi$
$191$	6.96830	+	4.02315i	0.504209	+	0.291105i	−0.226241	+	0.974071i	$0.572644\pi$
$192$	−5.60790	+	8.24675i	−0.404715	+	0.595158i
$193$	−3.76831	+	14.0635i	−0.271249	+	1.01231i	0.687065	+	0.726596i	$0.258899\pi$
$193$	−3.76831	+	14.0635i	−0.271249	+	1.01231i	−0.958314	+	0.285718i	$0.907768\pi$
$194$	−2.78245	−	5.50896i	−0.199768	−	0.395520i
$195$	9.55764	+	7.96972i	0.684437	+	0.570723i
$196$		0			0
$197$	16.4919	−	16.4919i	1.17500	−	1.17500i	0.194001	−	0.981001i	$-0.437854\pi$
$197$	16.4919	−	16.4919i	1.17500	−	1.17500i	0.981001	−	0.194001i	$-0.0621465\pi$
$198$	0.608257	−	1.84973i	0.0432269	−	0.131455i
$199$	4.82793	+	8.36222i	0.342243	+	0.592782i	0.984849	−	0.173415i	$-0.0554801\pi$
$199$	4.82793	+	8.36222i	0.342243	+	0.592782i	−0.642606	+	0.766197i	$0.722147\pi$
$200$	−3.48226	+	13.7067i	−0.246233	+	0.969211i
$201$	−9.28636	+	16.0844i	−0.655009	+	1.13451i
$202$	−1.97981	+	0.413507i	−0.139299	+	0.0290943i
$203$		0			0
$204$	−2.65399	−	6.07630i	−0.185816	−	0.425426i
$205$	7.79615	−	2.86482i	0.544507	−	0.200088i
$206$	14.3681	+	0.803980i	1.00107	+	0.0560159i
$207$	0.204725	−	0.764042i	0.0142293	−	0.0531046i
$208$	−8.33151	+	15.7949i	−0.577687	+	1.09518i
$209$			3.79066i			0.262205i
$210$		0			0
$211$		−	10.4344i		−	0.718333i	−0.933274	−	0.359166i	$-0.883061\pi$
$211$		−	10.4344i		−	0.718333i	0.933274	−	0.359166i	$-0.116939\pi$
$212$	4.59472	−	3.66721i	0.315567	−	0.251865i
$213$	2.45439	−	9.15992i	0.168172	−	0.627628i
$214$	0.00317820	−	0.0567984i	0.000217258	−	0.00388266i
$215$	−11.5942	+	25.0653i	−0.790716	+	1.70944i
$216$	−15.4563	−	2.61649i	−1.05167	−	0.178029i
$217$		0			0
$218$	−1.81951	−	8.71155i	−0.123233	−	0.590020i
$219$	9.17459	−	15.8909i	0.619961	−	1.07380i
$220$	−4.13595	+	1.01369i	−0.278846	+	0.0683429i
$221$	−5.93647	−	10.2823i	−0.399330	−	0.691660i
$222$	−1.74179	−	0.572761i	−0.116901	−	0.0384412i
$223$	10.7262	−	10.7262i	0.718279	−	0.718279i	−0.249973	−	0.968253i	$-0.580422\pi$
$223$	10.7262	−	10.7262i	0.718279	−	0.718279i	0.968253	+	0.249973i	$0.0804218\pi$
$224$		0			0
$225$	−7.11217	+	1.29934i	−0.474145	+	0.0866230i
$226$	19.3719	−	9.78431i	1.28860	−	0.650843i
$227$	−2.59397	+	9.68083i	−0.172168	+	0.642539i	0.824849	+	0.565353i	$0.191260\pi$
$227$	−2.59397	+	9.68083i	−0.172168	+	0.642539i	−0.997017	+	0.0771860i	$0.975406\pi$
$228$	9.81389	−	1.48327i	0.649941	−	0.0982316i
$229$	14.7989	+	8.54416i	0.977940	+	0.564614i	0.901647	−	0.432472i	$-0.142359\pi$
$229$	14.7989	+	8.54416i	0.977940	+	0.564614i	0.0762921	+	0.997086i	$0.475692\pi$
$230$	−1.65451	+	0.505012i	−0.109095	+	0.0332995i
$231$		0			0
$232$	−11.8450	−	16.6725i	−0.777661	−	1.09460i
$233$	1.81156	−	0.485407i	0.118680	−	0.0318001i	−0.198990	−	0.980001i	$-0.563766\pi$
$233$	1.81156	−	0.485407i	0.118680	−	0.0318001i	0.317670	+	0.948201i	$0.397100\pi$
$234$	−9.11508	−	0.510043i	−0.595871	−	0.0333425i
$235$	−5.86188	+	4.13153i	−0.382387	+	0.269512i
$236$	2.81175	−	25.0460i	0.183029	−	1.63036i
$237$	9.42947	−	9.42947i	0.612510	−	0.612510i
$238$		0			0
$239$	−15.2182			−0.984385			−0.492193	−	0.870486i	$-0.663804\pi$
$239$	−15.2182			−0.984385			−0.492193	+	0.870486i	$0.663804\pi$
$240$	4.24279	+	10.3112i	0.273871	+	0.665584i
$241$	−6.58780	−	11.4104i	−0.424357	−	0.735008i	0.572003	−	0.820252i	$-0.306167\pi$
$241$	−6.58780	−	11.4104i	−0.424357	−	0.735008i	−0.996360	+	0.0852432i	$0.972833\pi$
$242$	9.51365	+	10.6415i	0.611561	+	0.684058i
$243$	−3.47383	−	12.9645i	−0.222846	−	0.831673i
$244$	11.0402	−	4.82210i	0.706775	−	0.308703i
$245$		0			0
$246$	3.58599	−	5.47940i	0.228634	−	0.349354i
$247$	17.1670	−	4.59987i	1.09231	−	0.292683i
$248$	−4.64929	+	10.1511i	−0.295230	+	0.644598i
$249$	−8.73995	+	5.04601i	−0.553872	+	0.319778i
$250$	10.6468	+	11.6895i	0.673366	+	0.739310i
$251$			14.7048i			0.928161i	0.885793	+	0.464080i	$0.153615\pi$
$251$			14.7048i			0.928161i	−0.885793	+	0.464080i	$0.846385\pi$
$252$		0			0
$253$	−0.368320	−	0.368320i	−0.0231561	−	0.0231561i
$254$	2.18543	−	1.10381i	0.137126	−	0.0692592i
$255$	−7.30457	−	1.26478i	−0.457430	−	0.0792035i
$256$	−13.2052	+	9.03450i	−0.825326	+	0.564656i
$257$	−3.42109	−	12.7677i	−0.213402	−	0.796426i	−0.986723	−	0.162412i	$-0.948073\pi$
$257$	−3.42109	−	12.7677i	−0.213402	−	0.796426i	0.773321	−	0.634014i	$-0.218594\pi$
$258$	4.45165	+	21.3139i	0.277148	+	1.32694i
$259$		0			0
$260$	9.60963	+	17.5006i	0.595964	+	1.08534i
$261$	5.22778	−	9.05478i	0.323592	−	0.560477i
$262$	−1.37545	+	1.22968i	−0.0849755	+	0.0759697i
$263$	10.2083	+	2.73529i	0.629468	+	0.168665i	0.559428	−	0.828879i	$-0.311021\pi$
$263$	10.2083	+	2.73529i	0.629468	+	0.168665i	0.0700398	+	0.997544i	$0.477687\pi$
$264$	−2.14044	+	2.58661i	−0.131735	+	0.159195i
$265$	−0.593033	−	6.54585i	−0.0364298	−	0.402108i
$266$		0			0
$267$	−1.86676	−	1.86676i	−0.114244	−	0.114244i
$268$	−23.2889	+	18.5877i	−1.42260	+	1.13543i
$269$	10.5625	−	6.09826i	0.644007	−	0.371818i	−0.142149	−	0.989845i	$-0.545401\pi$
$269$	10.5625	−	6.09826i	0.644007	−	0.371818i	0.786156	+	0.618027i	$0.212068\pi$
$270$	−11.9589	+	12.8127i	−0.727794	+	0.779754i
$271$	5.70012	+	3.29096i	0.346257	+	0.199912i	0.663036	−	0.748588i	$-0.269268\pi$
$271$	5.70012	+	3.29096i	0.346257	+	0.199912i	−0.316778	+	0.948500i	$0.602601\pi$
$272$	−0.406362	−	10.6301i	−0.0246393	−	0.644546i
$273$		0			0
$274$	−0.898253	+	1.37253i	−0.0542655	+	0.0829178i
$275$	−1.60073	+	4.48383i	−0.0965278	+	0.270385i
$276$	−0.809446	+	1.09769i	−0.0487229	+	0.0660731i
$277$	3.96687	+	1.06292i	0.238346	+	0.0638646i	0.376015	−	0.926614i	$-0.377294\pi$
$277$	3.96687	+	1.06292i	0.238346	+	0.0638646i	−0.137669	+	0.990478i	$0.543961\pi$
$278$	−7.70948	+	23.4448i	−0.462384	+	1.40613i
$279$	−5.70799			−0.341728
$280$		0			0
$281$	−32.2773			−1.92550			−0.962752	−	0.270386i	$-0.912849\pi$
$281$	−32.2773			−1.92550			−0.962752	+	0.270386i	$0.912849\pi$
$282$	−1.76626	+	5.37126i	−0.105179	+	0.319854i
$283$	18.8626	+	5.05423i	1.12127	+	0.300443i	0.771396	−	0.636355i	$-0.219559\pi$
$283$	18.8626	+	5.05423i	1.12127	+	0.300443i	0.349872	+	0.936798i	$0.386225\pi$
$284$	9.02955	−	12.2450i	0.535805	−	0.726605i
$285$	4.65870	−	10.0716i	0.275958	−	0.596590i
$286$	−3.29208	+	5.03032i	−0.194665	+	0.297449i
$287$		0			0
$288$	−7.01036	−	4.21450i	−0.413090	−	0.248342i
$289$	−8.59722	−	4.96361i	−0.505719	−	0.291977i
$290$	−22.8522	+	0.787629i	−1.34193	+	0.0462512i
$291$	−4.71144	+	2.72015i	−0.276190	+	0.159458i
$292$	23.0086	−	18.3640i	1.34648	−	1.07467i
$293$	−12.6859	−	12.6859i	−0.741121	−	0.741121i	0.231673	−	0.972794i	$-0.425580\pi$
$293$	−12.6859	−	12.6859i	−0.741121	−	0.741121i	−0.972794	+	0.231673i	$0.925580\pi$
$294$		0			0
$295$	−21.6415	−	18.0460i	−1.26002	−	1.05068i
$296$	−2.26632	−	1.87540i	−0.131727	−	0.109006i
$297$	−5.09762	−	1.36590i	−0.295794	−	0.0792577i
$298$	11.8197	−	10.5671i	0.684699	−	0.612134i
$299$	−1.22108	+	2.11498i	−0.0706170	+	0.122312i
$300$	12.2348	+	2.38974i	0.706379	+	0.137972i
$301$		0			0
$302$	4.34295	+	20.7934i	0.249909	+	1.19653i
$303$	0.461430	+	1.72208i	0.0265085	+	0.0989309i
$304$	15.5274	+	3.53082i	0.890559	+	0.202506i
$305$	2.29801	−	13.2718i	0.131584	−	0.759944i
$306$	4.85436	−	2.45183i	0.277505	−	0.140162i
$307$	−9.98091	−	9.98091i	−0.569640	−	0.569640i	0.362387	−	0.932028i	$-0.381962\pi$
$307$	−9.98091	−	9.98091i	−0.569640	−	0.569640i	−0.932028	+	0.362387i	$0.881962\pi$
$308$		0			0
$309$		−	12.6850i		−	0.721626i
$310$	6.61021	+	10.5892i	0.375435	+	0.601429i
$311$	−12.0711	+	6.96926i	−0.684490	+	0.395190i	−0.801544	−	0.597935i	$-0.795988\pi$
$311$	−12.0711	+	6.96926i	−0.684490	+	0.395190i	0.117055	+	0.993125i	$0.462655\pi$
$312$	14.3115	+	6.55476i	0.810229	+	0.371090i
$313$	4.74109	−	1.27037i	0.267982	−	0.0718056i	−0.122326	−	0.992490i	$-0.539035\pi$
$313$	4.74109	−	1.27037i	0.267982	−	0.0718056i	0.390308	+	0.920684i	$0.372369\pi$
$314$	5.83006	−	8.90835i	0.329009	−	0.502727i
$315$		0			0
$316$	19.6060	−	8.56345i	1.10292	−	0.481732i
$317$	8.90414	+	33.2307i	0.500106	+	1.86642i	0.499312	+	0.866423i	$0.333586\pi$
$317$	8.90414	+	33.2307i	0.500106	+	1.86642i	0.000794747		1.00000i	$0.499747\pi$
$318$	−3.45381	−	3.86324i	−0.193680	−	0.216640i
$319$	−3.44258	−	5.96272i	−0.192747	−	0.333848i
$320$	0.299865	+	17.8860i	0.0167630	+	0.999859i
$321$	−0.0501451			−0.00279883
$322$		0			0
$323$	−7.48630	+	7.48630i	−0.416549	+	0.416549i
$324$	−0.573704	+	5.11034i	−0.0318724	+	0.283908i
$325$	22.2486	+	1.80831i	1.23413	+	0.100307i
$326$	9.38841	+	0.525337i	0.519976	+	0.0290957i
$327$	−7.57748	+	2.03038i	−0.419035	+	0.112280i
$328$	8.56473	−	6.08482i	0.472908	−	0.335978i
$329$		0			0
$330$	1.09584	+	3.59015i	0.0603239	+	0.197631i
$331$	−11.2201	−	6.47792i	−0.616712	−	0.356059i	0.158876	−	0.987299i	$-0.449213\pi$
$331$	−11.2201	−	6.47792i	−0.616712	−	0.356059i	−0.775588	+	0.631240i	$0.782546\pi$
$332$	−16.0094	+	2.41965i	−0.878630	+	0.132796i
$333$	0.389229	−	1.45262i	0.0213296	−	0.0796032i
$334$	−10.5909	+	5.34924i	−0.579510	+	0.292697i
$335$	3.00587	+	33.1785i	0.164228	+	1.81274i
$336$		0			0
$337$	7.43071	−	7.43071i	0.404776	−	0.404776i	−0.475136	−	0.879912i	$-0.657601\pi$
$337$	7.43071	−	7.43071i	0.404776	−	0.404776i	0.879912	+	0.475136i	$0.157601\pi$
$338$	9.31117	+	3.06184i	0.506461	+	0.166542i
$339$	−9.56524	−	16.5675i	−0.519513	−	0.899822i
$340$	−10.1702	−	6.16626i	−0.551556	−	0.334412i
$341$	−1.87940	+	3.25522i	−0.101775	+	0.176280i
$342$	1.66437	+	7.96877i	0.0899989	+	0.430902i
$343$		0			0
$344$	−5.83059	+	34.4429i	−0.314364	+	1.85704i
$345$	0.525944	+	1.43127i	0.0283159	+	0.0770571i
$346$	−0.174897	+	3.12562i	−0.00940251	+	0.168034i
$347$	−2.37153	+	8.85066i	−0.127310	+	0.475128i	−0.999911	−	0.0133050i	$-0.995765\pi$
$347$	−2.37153	+	8.85066i	−0.127310	+	0.475128i	0.872601	+	0.488433i	$0.162431\pi$
$348$	−14.0902	+	11.2459i	−0.755315	+	0.602844i
$349$		−	19.9513i		−	1.06797i	−0.845495	−	0.533984i	$-0.820694\pi$
$349$		−	19.9513i		−	1.06797i	0.845495	−	0.533984i	$-0.179306\pi$
$350$		0			0
$351$			24.7434i			1.32070i
$352$	−4.71171	+	2.61029i	−0.251135	+	0.139129i
$353$	−0.641552	+	2.39430i	−0.0341464	+	0.127436i	−0.980895	−	0.194537i	$-0.937679\pi$
$353$	−0.641552	+	2.39430i	−0.0341464	+	0.127436i	0.946749	+	0.321973i	$0.104346\pi$
$354$	−22.1816	−	1.24119i	−1.17894	−	0.0659687i
$355$	−5.86703	−	15.9662i	−0.311389	−	0.847396i
$356$	−1.69532	−	3.88142i	−0.0898516	−	0.205715i
$357$		0			0
$358$	22.7999	−	4.76203i	1.20501	−	0.251681i
$359$	7.94645	−	13.7637i	0.419398	−	0.726418i	−0.576481	−	0.817110i	$-0.695575\pi$
$359$	7.94645	−	13.7637i	0.419398	−	0.726418i	0.995879	+	0.0906921i	$0.0289079\pi$
$360$	−8.24957	+	3.94697i	−0.434790	+	0.208024i
$361$	1.57601	+	2.72973i	0.0829481	+	0.143670i
$362$	2.64019	−	8.02889i	0.138765	−	0.421989i
$363$	8.89708	−	8.89708i	0.466976	−	0.466976i
$364$		0			0
$365$	−2.96969	−	32.7792i	−0.155441	−	1.71574i
$366$	−4.78765	−	9.47905i	−0.250255	−	0.495478i
$367$	2.78634	−	10.3988i	0.145446	−	0.542812i	−0.854289	−	0.519798i	$-0.826007\pi$
$367$	2.78634	−	10.3988i	0.145446	−	0.542812i	0.999735	−	0.0230136i	$-0.00732610\pi$
$368$	−1.85180	+	1.16565i	−0.0965316	+	0.0607638i
$369$	4.65148	+	2.68553i	0.242147	+	0.139803i
$370$	−3.14560	+	0.960146i	−0.163532	+	0.0499156i
$371$		0			0
$372$	9.16305	+	3.59195i	0.475082	+	0.186234i
$373$	14.2618	−	3.82144i	0.738448	−	0.197867i	0.130060	−	0.991506i	$-0.458483\pi$
$373$	14.2618	−	3.82144i	0.738448	−	0.197867i	0.608388	+	0.793640i	$0.291816\pi$
$374$	0.200081	−	3.57568i	0.0103459	−	0.184894i
$375$	9.76368	−	9.94602i	0.504194	−	0.513610i
$376$	−5.78331	+	6.98880i	−0.298251	+	0.360420i
$377$	−22.8262	+	22.8262i	−1.17561	+	1.17561i
$378$		0			0
$379$	26.4563			1.35897			0.679483	−	0.733691i	$-0.262204\pi$
$379$	26.4563			1.35897			0.679483	+	0.733691i	$0.262204\pi$
$380$	12.8559	−	12.3160i	0.659495	−	0.631799i
$381$	−1.07909	−	1.86905i	−0.0552837	−	0.0957542i
$382$	8.48327	−	7.58420i	0.434042	−	0.388041i
$383$	−7.60437	−	28.3799i	−0.388565	−	1.45015i	−0.832470	−	0.554071i	$-0.813074\pi$
$383$	−7.60437	−	28.3799i	−0.388565	−	1.45015i	0.443904	−	0.896074i	$-0.353593\pi$
$384$	8.60163	+	11.1771i	0.438950	+	0.570377i
$385$		0			0
$386$	17.2288	+	11.2754i	0.876922	+	0.573901i
$387$	−17.2503	+	4.62219i	−0.876880	+	0.234959i
$388$	−8.63018	+	1.30436i	−0.438131	+	0.0662189i
$389$	−8.09963	+	4.67632i	−0.410667	+	0.237099i	−0.691076	−	0.722782i	$-0.742863\pi$
$389$	−8.09963	+	4.67632i	−0.410667	+	0.237099i	0.280409	+	0.959881i	$0.409530\pi$
$390$	14.9291	−	9.31935i	0.755967	−	0.471903i
$391$		−	1.45481i		−	0.0735731i
$392$		0			0
$393$	1.14998	+	1.14998i	0.0580090	+	0.0580090i
$394$	−14.8703	−	29.4416i	−0.749155	−	1.48325i
$395$	4.08098	−	23.5692i	0.205336	−	1.18589i
$396$	−2.21629	−	1.63432i	−0.111373	−	0.0821275i
$397$	4.59912	+	17.1641i	0.230823	+	0.861443i	0.979987	+	0.199059i	$0.0637886\pi$
$397$	4.59912	+	17.1641i	0.230823	+	0.861443i	−0.749164	+	0.662384i	$0.769545\pi$
$398$	13.3670	−	2.79186i	0.670028	−	0.139943i
$399$		0			0
$400$	16.8758	+	10.7335i	0.843790	+	0.536673i
$401$	−3.07671	+	5.32902i	−0.153644	+	0.266118i	−0.932564	−	0.361004i	$-0.882434\pi$
$401$	−3.07671	+	5.32902i	−0.153644	+	0.266118i	0.778921	+	0.627122i	$0.215767\pi$
$402$	17.5061	+	19.5813i	0.873124	+	0.976629i
$403$	17.0227	+	4.56121i	0.847960	+	0.227210i
$404$	−0.319102	+	2.84244i	−0.0158759	+	0.141417i
$405$	4.41569	+	3.68206i	0.219417	+	0.182963i
$406$		0			0
$407$	−0.700261	−	0.700261i	−0.0347107	−	0.0347107i
$408$	−9.33562	+	0.881145i	−0.462182	+	0.0436232i
$409$	−5.66917	+	3.27310i	−0.280322	+	0.161844i	−0.633569	−	0.773686i	$-0.718411\pi$
$409$	−5.66917	+	3.27310i	−0.280322	+	0.161844i	0.353247	+	0.935530i	$0.385078\pi$
$410$	−0.404608	−	11.7393i	−0.0199822	−	0.579762i
$411$	1.25221	+	0.722965i	0.0617670	+	0.0356612i
$412$	7.42751	−	18.9475i	0.365927	−	0.933478i
$413$		0			0
$414$	−0.936005	−	0.612568i	−0.0460022	−	0.0301061i
$415$	−7.59975	+	16.4298i	−0.373057	+	0.806508i
$416$	17.5389	+	18.1707i	0.859917	+	0.890890i
$417$	21.0136	+	5.63057i	1.02904	+	0.275730i
$418$	5.09253	+	1.67460i	0.249084	+	0.0819076i
$419$	−17.7908			−0.869139			−0.434569	−	0.900638i	$-0.643099\pi$
$419$	−17.7908			−0.869139			−0.434569	+	0.900638i	$0.643099\pi$
$420$		0			0
$421$	−16.4678			−0.802591			−0.401295	−	0.915949i	$-0.631440\pi$
$421$	−16.4678			−0.802591			−0.401295	+	0.915949i	$0.631440\pi$
$422$	−14.0180	−	4.60961i	−0.682385	−	0.224392i
$423$	−4.47954	−	1.20029i	−0.217803	−	0.0583601i
$424$	−2.89687	−	7.79281i	−0.140684	−	0.378452i
$425$	−12.0166	+	5.69392i	−0.582891	+	0.276196i
$426$	−11.2215	−	7.34393i	−0.543686	−	0.355815i
$427$		0			0
$428$	−0.0749013	−	0.0293616i	−0.00362049	−	0.00141925i
$429$	4.58934	+	2.64965i	0.221575	+	0.127926i
$430$	28.5518	+	26.6492i	1.37689	+	1.28514i
$431$	13.1055	−	7.56644i	0.631268	−	0.364463i	−0.149975	−	0.988690i	$-0.547919\pi$
$431$	13.1055	−	7.56644i	0.631268	−	0.364463i	0.781243	+	0.624227i	$0.214586\pi$
$432$	−10.3433	+	19.6088i	−0.497640	+	0.943427i
$433$	5.45382	+	5.45382i	0.262094	+	0.262094i	0.825904	−	0.563811i	$-0.190665\pi$
$433$	5.45382	+	5.45382i	0.262094	+	0.262094i	−0.563811	+	0.825904i	$0.690665\pi$
$434$		0			0
$435$	1.81860	+	20.0736i	0.0871953	+	0.962454i
$436$	−12.5073	−	1.40411i	−0.598990	−	0.0672446i
$437$	2.10350	+	0.563632i	0.100624	+	0.0269622i
$438$	−17.2954	−	19.3457i	−0.826405	−	0.924371i
$439$	12.8732	−	22.2970i	0.614402	−	1.06418i	−0.376087	−	0.926585i	$-0.622730\pi$
$439$	12.8732	−	22.2970i	0.614402	−	1.06418i	0.990489	−	0.137592i	$-0.0439362\pi$
$440$	−0.465312	+	6.00423i	−0.0221829	+	0.286241i
$441$		0			0
$442$	−16.4362	+	3.43289i	−0.781790	+	0.163286i
$443$	−4.47481	−	16.7002i	−0.212605	−	0.793452i	−0.986996	−	0.160745i	$-0.948610\pi$
$443$	−4.47481	−	16.7002i	−0.212605	−	0.793452i	0.774391	−	0.632707i	$-0.218056\pi$
$444$	−1.53894	+	2.08696i	−0.0730351	+	0.0990428i
$445$	−4.66601	−	0.807916i	−0.221190	−	0.0382989i
$446$	−9.67150	−	19.1486i	−0.457959	−	0.906711i
$447$	−9.88223	−	9.88223i	−0.467413	−	0.467413i
$448$		0			0
$449$			11.0999i			0.523839i	0.965090	+	0.261919i	$0.0843555\pi$
$449$			11.0999i			0.523839i	−0.965090	+	0.261919i	$0.915645\pi$
$450$	−1.39636	+	10.1288i	−0.0658250	+	0.477476i
$451$	3.06308	−	1.76847i	0.144235	−	0.0832739i
$452$	−4.58670	−	30.3475i	−0.215740	−	1.42743i
$453$	18.0865	−	4.84627i	0.849779	−	0.227698i
$454$	11.8597	+	7.76157i	0.556603	+	0.364268i
$455$		0			0
$456$	2.34281	−	13.8397i	0.109712	−	0.648101i
$457$	−5.49672	−	20.5140i	−0.257126	−	0.959606i	−0.966896	−	0.255172i	$-0.917868\pi$
$457$	−5.49672	−	20.5140i	−0.257126	−	0.959606i	0.709770	−	0.704434i	$-0.248799\pi$
$458$	18.0163	−	16.1069i	0.841847	−	0.752627i
$459$	−7.36989	−	12.7650i	−0.343997	−	0.595821i
$460$	−0.0524592	+	2.44584i	−0.00244592	+	0.114038i
$461$	8.61652			0.401311			0.200656	−	0.979662i	$-0.435693\pi$
$461$	8.61652			0.401311			0.200656	+	0.979662i	$0.435693\pi$
$462$		0			0
$463$	1.63340	−	1.63340i	0.0759103	−	0.0759103i	−0.668132	−	0.744043i	$-0.732906\pi$
$463$	1.63340	−	1.63340i	0.0759103	−	0.0759103i	0.744043	+	0.668132i	$0.232906\pi$
$464$	−27.6313	+	8.54761i	−1.28275	+	0.396813i
$465$	8.99413	−	6.33918i	0.417093	−	0.293972i
$466$	0.148181	−	2.64817i	0.00686435	−	0.122674i
$467$	24.6125	−	6.59489i	1.13893	−	0.305175i	0.360409	−	0.932794i	$-0.382637\pi$
$467$	24.6125	−	6.59489i	1.13893	−	0.305175i	0.778521	+	0.627619i	$0.215970\pi$
$468$	−4.71199	+	12.0203i	−0.217812	+	0.555637i
$469$		0			0
$470$	2.96086	+	9.70030i	0.136574	+	0.447441i
$471$	−8.12741	−	4.69236i	−0.374491	−	0.216213i
$472$	−32.4058	−	14.8421i	−1.49160	−	0.683161i
$473$	−3.04379	+	11.3596i	−0.139953	+	0.522313i
$474$	−8.50228	−	16.8336i	−0.390523	−	0.773194i
$475$	−3.57726	−	19.5807i	−0.164136	−	0.898423i
$476$		0			0
$477$	3.00540	−	3.00540i	0.137608	−	0.137608i
$478$	−6.72298	+	20.4448i	−0.307502	+	0.935124i
$479$	−4.63924	−	8.03541i	−0.211972	−	0.367147i	0.740359	−	0.672211i	$-0.234655\pi$
$479$	−4.63924	−	8.03541i	−0.211972	−	0.367147i	−0.952332	+	0.305064i	$0.901322\pi$
$480$	15.7268	−	1.14475i	0.717828	−	0.0522504i
$481$	−2.32156	+	4.02106i	−0.105854	+	0.183345i
$482$	−18.2395	+	3.80954i	−0.830787	+	0.173520i
$483$		0			0
$484$	18.4990	−	8.07996i	0.840865	−	0.367271i
$485$	−4.09679	+	8.85680i	−0.186026	+	0.402167i
$486$	−18.9517	−	1.06046i	−0.859666	−	0.0481034i
$487$	4.60932	−	17.2022i	0.208868	−	0.779506i	−0.779368	−	0.626567i	$-0.784459\pi$
$487$	4.60932	−	17.2022i	0.208868	−	0.779506i	0.988236	−	0.152939i	$-0.0488738\pi$
$488$	−1.60097	−	16.9621i	−0.0724727	−	0.767839i
$489$		−	8.28866i		−	0.374826i
$490$		0			0
$491$		−	2.49970i		−	0.112810i	−0.998408	−	0.0564049i	$-0.982036\pi$
$491$		−	2.49970i		−	0.112810i	0.998408	−	0.0564049i	$-0.0179638\pi$
$492$	−5.77707	−	7.23821i	−0.260450	−	0.326324i
$493$	4.97711	−	18.5748i	0.224158	−	0.836569i
$494$	1.40421	−	25.0949i	0.0631784	−	1.12907i
$495$	−2.88982	+	1.06191i	−0.129888	+	0.0477293i
$496$	11.5836	+	10.7305i	0.520117	+	0.481816i
$497$		0			0
$498$	2.91797	+	13.9708i	0.130757	+	0.626047i
$499$	3.26199	−	5.64993i	0.146027	−	0.252926i	−0.783729	−	0.621103i	$-0.786685\pi$
$499$	3.26199	−	5.64993i	0.146027	−	0.252926i	0.929756	+	0.368178i	$0.120018\pi$
$500$	20.4077	−	9.13933i	0.912658	−	0.408723i
$501$	5.22947	+	9.05770i	0.233635	+	0.404668i
$502$	19.7551	+	6.49618i	0.881713	+	0.289938i
$503$	−14.6078	+	14.6078i	−0.651327	+	0.651327i	−0.953313	−	0.301985i	$-0.902351\pi$
$503$	−14.6078	+	14.6078i	−0.651327	+	0.651327i	0.301985	+	0.953313i	$0.402351\pi$
$504$		0			0
$505$	2.45607	+	2.04801i	0.109294	+	0.0911353i
$506$	−0.657529	+	0.332103i	−0.0292308	+	0.0147638i
$507$	2.23620	−	8.34561i	0.0993131	−	0.370641i
$508$	−0.517445	−	3.42363i	−0.0229579	−	0.151899i
$509$	29.8459	+	17.2316i	1.32290	+	0.763775i	0.984190	−	0.177116i	$-0.0566769\pi$
$509$	29.8459	+	17.2316i	1.32290	+	0.763775i	0.338708	+	0.940892i	$0.390010\pi$
$510$	−4.92611	+	9.25452i	−0.218132	+	0.409797i
$511$		0			0
$512$	6.30364	+	21.7316i	0.278584	+	0.960412i
$513$	21.3121	−	5.71056i	0.940953	−	0.252128i
$514$	−18.6640	−	1.04436i	−0.823233	−	0.0460648i
$515$	−13.1083	−	18.5982i	−0.577620	−	0.819536i
$516$	30.6006	+	3.43532i	1.34711	+	0.151232i
$517$	−2.15944	+	2.15944i	−0.0949721	+	0.0949721i
$518$		0			0
$519$	2.75949			0.121128
$520$	27.7563	−	5.17871i	1.21720	−	0.227101i
$521$	−16.9526	−	29.3627i	−0.742705	−	1.28640i	−0.951259	−	0.308392i	$-0.900209\pi$
$521$	−16.9526	−	29.3627i	−0.742705	−	1.28640i	0.208555	−	0.978011i	$-0.433124\pi$
$522$	−9.85510	−	11.0234i	−0.431346	−	0.482480i
$523$	4.77618	+	17.8250i	0.208848	+	0.779431i	0.988242	+	0.152897i	$0.0488604\pi$
$523$	4.77618	+	17.8250i	0.208848	+	0.779431i	−0.779394	+	0.626534i	$0.784473\pi$
$524$	1.04437	+	2.39107i	0.0456233	+	0.104455i
$525$		0			0
$526$	8.18443	−	12.5058i	0.356858	−	0.545280i
$527$	−10.1405	+	2.71715i	−0.441728	+	0.118361i
$528$	2.52937	+	4.01825i	0.110077	+	0.174872i
$529$	19.6594	−	11.3504i	0.854758	−	0.493495i
$530$	−9.05596	−	2.09506i	−0.393366	−	0.0910038i
$531$		−	18.2217i		−	0.790756i
$532$		0			0
$533$	−11.7259	−	11.7259i	−0.507906	−	0.507906i
$534$	−3.33257	+	1.68321i	−0.144214	+	0.0728394i
$535$	−0.0735205	+	0.0518182i	−0.00317857	+	0.00224030i
$536$	14.6832	+	39.4989i	0.634216	+	1.70609i
$537$	−5.31392	−	19.8318i	−0.229312	−	0.855806i
$538$	−3.52645	−	16.8842i	−0.152036	−	0.727928i
$539$		0			0
$540$	11.9300	+	21.7263i	0.513385	+	0.934953i
$541$	−1.59149	+	2.75655i	−0.0684236	+	0.118513i	−0.898208	−	0.439572i	$-0.855130\pi$
$541$	−1.59149	+	2.75655i	−0.0684236	+	0.118513i	0.829784	+	0.558085i	$0.188464\pi$
$542$	6.93937	−	6.20392i	0.298071	−	0.266481i
$543$	−7.19630	−	1.92824i	−0.308823	−	0.0827488i
$544$	−14.4605	−	4.15016i	−0.619988	−	0.177937i
$545$	−9.01164	+	10.8072i	−0.386016	+	0.462928i
$546$		0			0
$547$	−15.6791	−	15.6791i	−0.670391	−	0.670391i	0.287415	−	0.957806i	$-0.407204\pi$
$547$	−15.6791	−	15.6791i	−0.670391	−	0.670391i	−0.957806	+	0.287415i	$0.907204\pi$
$548$	1.44710	+	1.81310i	0.0618169	+	0.0774517i
$549$	7.54315	−	4.35504i	0.321934	−	0.185869i
$550$	5.31661	+	4.13132i	0.226701	+	0.176160i
$551$	24.9289	+	14.3927i	1.06201	+	0.613151i
$552$	1.11709	+	1.57237i	0.0475466	+	0.0669246i
$553$		0			0
$554$	3.18042	−	4.85969i	0.135123	−	0.206469i
$555$	0.999942	+	2.72118i	0.0424452	+	0.115508i
$556$	28.0909	+	20.7145i	1.19132	+	0.878490i
$557$	−20.6171	−	5.52434i	−0.873575	−	0.234074i	−0.205942	−	0.978564i	$-0.566026\pi$
$557$	−20.6171	−	5.52434i	−0.873575	−	0.234074i	−0.667633	+	0.744491i	$0.732692\pi$
$558$	−2.52163	+	7.66835i	−0.106749	+	0.324627i
$559$	55.1382			2.33210
$560$		0			0
$561$	−3.15683			−0.133282
$562$	−14.2592	+	43.3627i	−0.601488	+	1.82915i
$563$	−13.1487	−	3.52319i	−0.554153	−	0.148485i	−0.0291340	−	0.999576i	$-0.509275\pi$
$563$	−13.1487	−	3.52319i	−0.554153	−	0.148485i	−0.525019	+	0.851091i	$0.675942\pi$
$564$	6.43570	+	4.74574i	0.270992	+	0.199832i
$565$	−31.1444	−	14.4061i	−1.31025	−	0.606070i
$566$	15.1231	−	23.1081i	0.635669	−	0.971305i
$567$		0			0
$568$	−12.4614	−	17.5402i	−0.522869	−	0.735969i
$569$	20.3421	+	11.7445i	0.852787	+	0.492357i	0.861590	−	0.507605i	$-0.169469\pi$
$569$	20.3421	+	11.7445i	0.852787	+	0.492357i	−0.00880335	+	0.999961i	$0.502802\pi$
$570$	−11.4725	−	10.7080i	−0.480531	−	0.448511i
$571$	−23.4830	+	13.5579i	−0.982734	+	0.567382i	−0.903094	−	0.429442i	$-0.858710\pi$
$571$	−23.4830	+	13.5579i	−0.982734	+	0.567382i	−0.0796395	+	0.996824i	$0.525377\pi$
$572$	5.30359	+	6.64498i	0.221754	+	0.277840i
$573$	−7.09267	−	7.09267i	−0.296301	−	0.296301i
$574$		0			0
$575$	2.25014	+	1.55497i	0.0938374	+	0.0648469i
$576$	−8.75892	+	7.55617i	−0.364955	+	0.314841i
$577$	26.9522	+	7.22183i	1.12204	+	0.300649i	0.771707	−	0.635978i	$-0.219403\pi$
$577$	26.9522	+	7.22183i	1.12204	+	0.300649i	0.350329	+	0.936627i	$0.386070\pi$
$578$	−10.4663	+	9.35709i	−0.435342	+	0.389204i
$579$	9.07505	−	15.7184i	0.377146	−	0.653236i
$580$	−9.03732	+	31.0486i	−0.375254	+	1.28922i
$581$		0			0
$582$	1.57299	+	7.53124i	0.0652024	+	0.312180i
$583$	−0.724403	−	2.70351i	−0.0300017	−	0.111968i
$584$	−14.5064	−	39.0235i	−0.600280	−	1.61480i
$585$	8.31585	+	11.7987i	0.343818	+	0.487815i
$586$	−22.6471	+	11.4385i	−0.935544	+	0.472522i
$587$	22.8296	+	22.8296i	0.942280	+	0.942280i	0.998423	−	0.0561427i	$-0.0178802\pi$
$587$	22.8296	+	22.8296i	0.942280	+	0.942280i	−0.0561427	+	0.998423i	$0.517880\pi$
$588$		0			0
$589$		−	15.7148i		−	0.647516i
$590$	−33.8043	+	21.1019i	−1.39170	+	0.868753i
$591$	−25.1794	+	14.5374i	−1.03574	+	0.597987i
$592$	−3.52069	+	2.21617i	−0.144700	+	0.0910842i
$593$	36.8872	−	9.88391i	1.51478	−	0.405883i	0.596759	−	0.802421i	$-0.296455\pi$
$593$	36.8872	−	9.88391i	1.51478	−	0.405883i	0.918019	+	0.396537i	$0.129788\pi$
$594$	−4.08700	+	6.24494i	−0.167691	+	0.256233i
$595$		0			0
$596$	−8.97462	−	20.5474i	−0.367615	−	0.841653i
$597$	−3.11542	−	11.6269i	−0.127506	−	0.475857i
$598$	2.30191	+	2.57479i	0.0941321	+	0.105291i
$599$	−14.4801	−	25.0802i	−0.591640	−	1.02475i	−0.994012	−	0.109274i	$-0.965147\pi$
$599$	−14.4801	−	25.0802i	−0.591640	−	1.02475i	0.402372	−	0.915476i	$-0.368186\pi$
$600$	8.61549	−	15.3811i	0.351726	−	0.627930i
$601$	8.88262			0.362330			0.181165	−	0.983453i	$-0.442013\pi$
$601$	8.88262			0.362330			0.181165	+	0.983453i	$0.442013\pi$
$602$		0			0
$603$	−15.2333	+	15.2333i	−0.620347	+	0.620347i
$604$	29.8534	+	3.35144i	1.21472	+	0.136368i
$605$	3.85057	−	22.2384i	0.156548	−	0.904121i
$606$	2.51736	+	0.140861i	0.102261	+	0.00572210i
$607$	−44.3709	+	11.8891i	−1.80096	+	0.482565i	−0.994127	−	0.108218i	$-0.965485\pi$
$607$	−44.3709	+	11.8891i	−1.80096	+	0.482565i	−0.806830	+	0.590783i	$0.798819\pi$
$608$	11.6030	−	19.3004i	0.470565	−	0.782734i
$609$		0			0
$610$	−16.8148	−	8.95037i	−0.680810	−	0.362390i
$611$	12.4000	+	7.15915i	0.501651	+	0.289628i
$612$	−1.14937	−	7.60470i	−0.0464605	−	0.307402i
$613$	0.0600047	−	0.223941i	0.00242357	−	0.00904487i	−0.964703	−	0.263339i	$-0.915176\pi$
$613$	0.0600047	−	0.223941i	0.00242357	−	0.00904487i	0.967127	+	0.254294i	$0.0818430\pi$
$614$	−17.8181	+	8.99949i	−0.719078	+	0.363190i
$615$	−10.3119	+	0.934224i	−0.415815	+	0.0376716i
$616$		0			0
$617$	−27.1038	+	27.1038i	−1.09116	+	1.09116i	−0.0957517	+	0.995405i	$0.530525\pi$
$617$	−27.1038	+	27.1038i	−1.09116	+	1.09116i	−0.995405	+	0.0957517i	$0.969475\pi$
$618$	−17.0416	−	5.60389i	−0.685514	−	0.225421i
$619$	−7.14970	−	12.3836i	−0.287371	−	0.497741i	0.685811	−	0.727780i	$-0.259448\pi$
$619$	−7.14970	−	12.3836i	−0.287371	−	0.497741i	−0.973181	+	0.230039i	$0.926115\pi$
$620$	17.1463	−	4.20241i	0.688610	−	0.168773i
$621$	−1.51593	+	2.62566i	−0.0608320	+	0.105364i
$622$	4.03012	+	19.2957i	0.161593	+	0.773685i
$623$		0			0
$624$	15.1284	−	16.3310i	0.605619	−	0.653762i
$625$	4.03719	−	24.6719i	0.161488	−	0.986875i
$626$	0.387808	−	6.93059i	0.0154999	−	0.277002i
$627$	1.22304	−	4.56444i	0.0488434	−	0.182286i
$628$	−9.39230	−	11.7678i	−0.374794	−	0.469587i
$629$		−	2.76594i		−	0.110285i
$630$		0			0
$631$			30.7128i			1.22266i	0.791377	+	0.611328i	$0.209364\pi$
$631$			30.7128i			1.22266i	−0.791377	+	0.611328i	$0.790636\pi$
$632$	−2.84313	−	30.1226i	−0.113094	−	1.19821i
$633$	−3.36660	+	12.5643i	−0.133810	+	0.499387i
$634$	48.5771	+	2.71818i	1.92924	+	0.107953i
$635$	−3.51353	−	1.62521i	−0.139430	−	0.0644946i
$636$	−6.71584	+	2.93332i	−0.266300	+	0.116314i
$637$		0			0
$638$	−9.53141	+	1.99075i	−0.377352	+	0.0788144i
$639$	5.49985	−	9.52602i	0.217571	−	0.376843i
$640$	24.1613	+	7.49869i	0.955060	+	0.296412i
$641$	−20.7752	−	35.9837i	−0.820572	−	1.42127i	−0.905257	−	0.424864i	$-0.860322\pi$
$641$	−20.7752	−	35.9837i	−0.820572	−	1.42127i	0.0846851	−	0.996408i	$-0.473012\pi$
$642$	−0.0221527	+	0.0673670i	−0.000874296	+	0.00265876i
$643$	−12.5692	+	12.5692i	−0.495681	+	0.495681i	−0.910090	−	0.414410i	$-0.863988\pi$
$643$	−12.5692	+	12.5692i	−0.495681	+	0.495681i	0.414410	+	0.910090i	$0.363988\pi$
$644$		0			0
$645$	22.0481	−	26.4410i	0.868142	−	1.04111i
$646$	6.75018	+	13.3646i	0.265582	+	0.525825i
$647$	−9.22084	+	34.4127i	−0.362509	+	1.35290i	0.508258	+	0.861205i	$0.330290\pi$
$647$	−9.22084	+	34.4127i	−0.362509	+	1.35290i	−0.870767	+	0.491696i	$0.836377\pi$
$648$	6.61200	+	3.02834i	0.259744	+	0.118964i
$649$	−10.3917	−	5.99966i	−0.407910	−	0.235507i
$650$	12.2582	−	29.0909i	0.480805	−	1.14104i
$651$		0			0
$652$	4.85329	−	12.3807i	0.190070	−	0.484866i
$653$	−12.7132	+	3.40648i	−0.497505	+	0.133306i	−0.498842	−	0.866693i	$-0.666241\pi$
$653$	−12.7132	+	3.40648i	−0.497505	+	0.133306i	0.00133684	+	0.999999i	$0.499574\pi$
$654$	−0.619816	+	11.0769i	−0.0242367	+	0.433140i
$655$	2.87441	+	0.497701i	0.112312	+	0.0194468i
$656$	−4.39095	−	14.1943i	−0.171438	−	0.554195i
$657$	15.0499	−	15.0499i	0.587153	−	0.587153i
$658$		0			0
$659$	10.3786			0.404294			0.202147	−	0.979355i	$-0.435208\pi$
$659$	10.3786			0.404294			0.202147	+	0.979355i	$0.435208\pi$
$660$	5.30727	+	0.113832i	0.206585	+	0.00443092i
$661$	11.5282	+	19.9675i	0.448397	+	0.776646i	0.998282	−	0.0585946i	$-0.0186619\pi$
$661$	11.5282	+	19.9675i	0.448397	+	0.776646i	−0.549885	+	0.835240i	$0.685329\pi$
$662$	−13.6594	+	12.2118i	−0.530889	+	0.474624i
$663$	3.83074	+	14.2965i	0.148774	+	0.555231i
$664$	−3.82184	+	22.5767i	−0.148316	+	0.876144i
$665$		0			0
$666$	−1.77956	−	1.16463i	−0.0689567	−	0.0451286i
$667$	−3.82069	+	1.02375i	−0.147938	+	0.0396398i
$668$	2.50762	+	16.5914i	0.0970228	+	0.641942i
$669$	−16.3765	+	9.45496i	−0.633151	+	0.365550i
$670$	45.9013	+	10.6191i	1.77332	+	0.410252i
$671$		−	5.73573i		−	0.221425i
$672$		0			0
$673$	27.9624	+	27.9624i	1.07787	+	1.07787i	0.996700	+	0.0811716i	$0.0258662\pi$
$673$	27.9624	+	27.9624i	1.07787	+	1.07787i	0.0811716	+	0.996700i	$0.474134\pi$
$674$	−6.70005	−	13.2654i	−0.258076	−	0.510964i
$675$	27.6208	+	2.24494i	1.06312	+	0.0864079i
$676$	8.22682	−	11.1564i	0.316416	−	0.429092i
$677$	8.86132	+	33.0709i	0.340568	+	1.27102i	0.897705	+	0.440597i	$0.145233\pi$
$677$	8.86132	+	33.0709i	0.340568	+	1.27102i	−0.557137	+	0.830421i	$0.688100\pi$
$678$	−26.4831	+	5.53131i	−1.01708	+	0.212429i
$679$		0			0
$680$	−12.7769	+	10.9390i	−0.489973	+	0.419492i
$681$	6.24694	−	10.8200i	0.239383	−	0.414624i
$682$	3.54293	+	3.96293i	0.135666	+	0.151748i
$683$	−1.86138	−	0.498756i	−0.0712239	−	0.0190844i	0.223031	−	0.974811i	$-0.428405\pi$
$683$	−1.86138	−	0.498756i	−0.0712239	−	0.0190844i	−0.294255	+	0.955727i	$0.595072\pi$
$684$	11.4409	+	1.28439i	0.437452	+	0.0491099i
$685$	2.58302	−	0.234014i	0.0986922	−	0.00894120i
$686$		0			0
$687$	−15.0630	−	15.0630i	−0.574691	−	0.574691i
$688$	43.6963	+	23.0490i	1.66591	+	0.878734i
$689$	−11.3645	+	6.56128i	−0.432952	+	0.249965i
$690$	2.15518	−	0.0742808i	0.0820462	−	0.00282782i
$691$	30.8812	+	17.8293i	1.17478	+	0.678257i	0.954800	−	0.297248i	$-0.0960688\pi$
$691$	30.8812	+	17.8293i	1.17478	+	0.678257i	0.219976	+	0.975505i	$0.429402\pi$
$692$	4.12182	+	1.61577i	0.156688	+	0.0614225i
$693$		0			0
$694$	10.8427	+	7.09598i	0.411582	+	0.269360i
$695$	36.6276	−	13.4594i	1.38936	−	0.510544i
$696$	8.88357	+	23.8975i	0.336731	+	0.905833i
$697$	9.54198	+	2.55677i	0.361428	+	0.0968444i
$698$	−26.8034	−	8.81390i	−1.01452	−	0.333611i
$699$	−2.33797			−0.0884301
$700$		0			0
$701$	33.6504			1.27096			0.635479	−	0.772119i	$-0.280803\pi$
$701$	33.6504			1.27096			0.635479	+	0.772119i	$0.280803\pi$
$702$	33.2413	+	10.9309i	1.25461	+	0.412561i
$703$	3.99924	+	1.07159i	0.150834	+	0.0404159i
$704$	1.42528	+	7.48307i	0.0537173	+	0.282029i
$705$	8.39147	−	3.08359i	0.316041	−	0.116135i
$706$	2.93319	+	1.91962i	0.110392	+	0.0722460i
$707$		0			0
$708$	−11.4667	+	29.2514i	−0.430944	+	1.09934i
$709$	7.92917	+	4.57791i	0.297786	+	0.171927i	0.641448	−	0.767167i	$-0.278334\pi$
$709$	7.92917	+	4.57791i	0.297786	+	0.171927i	−0.343662	+	0.939093i	$0.611667\pi$
$710$	−24.0415	+	0.828619i	−0.902261	+	0.0310975i
$711$	13.3957	−	7.73401i	0.502378	−	0.290048i
$712$	−5.96341	+	0.562858i	−0.223488	+	0.0210940i
$713$	1.52693	+	1.52693i	0.0571839	+	0.0571839i
$714$		0			0
$715$	9.46674	−	0.857657i	0.354036	−	0.0320745i
$716$	3.67484	−	32.7341i	0.137335	−	1.22333i
$717$	18.3247	+	4.91009i	0.684348	+	0.183370i
$718$	−14.9802	−	16.7560i	−0.559055	−	0.625328i
$719$	6.67322	−	11.5584i	0.248869	−	0.431054i	−0.714343	−	0.699796i	$-0.753274\pi$
$719$	6.67322	−	11.5584i	0.248869	−	0.431054i	0.963212	+	0.268742i	$0.0866078\pi$
$720$	1.65811	+	12.8265i	0.0617939	+	0.478015i
$721$		0			0
$722$	4.36348	−	0.911364i	0.162392	−	0.0339175i
$723$	4.25104	+	15.8651i	0.158098	+	0.590029i
$724$	−9.62000	−	7.09387i	−0.357524	−	0.263642i
$725$	23.4097	+	27.5517i	0.869414	+	1.02324i
$726$	−8.02224	−	15.8832i	−0.297733	−	0.589481i
$727$	−6.15934	−	6.15934i	−0.228437	−	0.228437i	0.583602	−	0.812040i	$-0.301643\pi$
$727$	−6.15934	−	6.15934i	−0.228437	−	0.228437i	−0.812040	+	0.583602i	$0.801643\pi$
$728$		0			0
$729$			24.4454i			0.905384i
$730$	−45.3488	−	10.4913i	−1.67844	−	0.388300i
$731$	−28.4457	+	16.4231i	−1.05210	+	0.607431i
$732$	−14.8496	+	2.24436i	−0.548857	+	0.0829540i
$733$	9.92223	−	2.65865i	0.366486	−	0.0981996i	−0.0708761	−	0.997485i	$-0.522580\pi$
$733$	9.92223	−	2.65865i	0.366486	−	0.0981996i	0.437362	+	0.899286i	$0.355913\pi$
$734$	−12.7392	−	8.33717i	−0.470213	−	0.307731i
$735$		0			0
$736$	0.747914	+	3.00273i	0.0275685	+	0.110682i
$737$	3.67173	+	13.7031i	0.135250	+	0.504760i
$738$	5.66275	−	5.06261i	0.208449	−	0.186357i
$739$	21.8583	+	37.8597i	0.804070	+	1.39269i	0.916917	+	0.399078i	$0.130670\pi$
$739$	21.8583	+	37.8597i	0.804070	+	1.39269i	−0.112847	+	0.993612i	$0.535997\pi$
$740$	−0.0997371	+	4.65010i	−0.00366641	+	0.170941i
$741$	−22.1553			−0.813897
$742$		0			0
$743$	26.0186	−	26.0186i	0.954529	−	0.954529i	−0.0444813	−	0.999010i	$-0.514164\pi$
$743$	26.0186	−	26.0186i	0.954529	−	0.954529i	0.999010	+	0.0444813i	$0.0141635\pi$
$744$	8.87356	−	10.7232i	0.325320	−	0.393132i
$745$	−24.7008	−	4.27693i	−0.904969	−	0.156694i
$746$	1.16658	−	20.8481i	0.0427114	−	0.763304i
$747$	−11.3072	+	3.02975i	−0.413709	+	0.110853i
$748$	−4.71534	−	1.84843i	−0.172410	−	0.0675854i
$749$		0			0
$750$	−9.04860	−	17.5108i	−0.330408	−	0.639405i
$751$	7.30460	+	4.21731i	0.266548	+	0.153892i	0.627318	−	0.778763i	$-0.284153\pi$
$751$	7.30460	+	4.21731i	0.266548	+	0.153892i	−0.360770	+	0.932655i	$0.617486\pi$
$752$	6.83416	+	10.8570i	0.249216	+	0.395914i
$753$	4.74444	−	17.7065i	0.172897	−	0.645260i
$754$	20.5817	+	40.7497i	0.749542	+	1.48402i
$755$	21.5097	−	25.7954i	0.782818	−	0.938790i
$756$		0			0
$757$	3.33081	−	3.33081i	0.121060	−	0.121060i	−0.643981	−	0.765041i	$-0.722718\pi$
$757$	3.33081	−	3.33081i	0.121060	−	0.121060i	0.765041	+	0.643981i	$0.222718\pi$
$758$	11.6876	−	35.5425i	0.424514	−	1.29096i
$759$	0.324667	+	0.562340i	0.0117847	+	0.0204117i
$760$	−10.8665	−	22.7121i	−0.394169	−	0.823853i
$761$	−17.2317	+	29.8462i	−0.624649	+	1.08192i	0.363959	+	0.931415i	$0.381425\pi$
$761$	−17.2317	+	29.8462i	−0.624649	+	1.08192i	−0.988609	+	0.150509i	$0.951909\pi$
$762$	−2.98767	+	0.624010i	−0.108232	+	0.0226055i
$763$		0			0
$764$	−6.44127	−	14.7473i	−0.233037	−	0.533537i
$765$	−7.80440	−	3.60999i	−0.282169	−	0.130520i
$766$	−41.4862	−	2.32140i	−1.49896	−	0.0838755i
$767$	−14.5609	+	54.3419i	−0.525763	+	1.96217i
$768$	18.8157	−	6.61809i	0.678953	−	0.238810i
$769$			18.7498i			0.676135i	0.941122	+	0.338067i	$0.109773\pi$
$769$			18.7498i			0.676135i	−0.941122	+	0.338067i	$0.890227\pi$
$770$		0			0
$771$			16.4777i			0.593431i
$772$	22.7590	−	18.1648i	0.819114	−	0.653764i
$773$	−11.5075	+	42.9466i	−0.413896	+	1.54468i	0.373140	+	0.927775i	$0.378281\pi$
$773$	−11.5075	+	42.9466i	−0.413896	+	1.54468i	−0.787036	+	0.616907i	$0.788386\pi$
$774$	−1.41102	+	25.2167i	−0.0507181	+	0.906395i
$775$	6.63610	−	18.5884i	0.238376	−	0.667716i
$776$	−2.06023	+	12.1704i	−0.0739581	+	0.436891i
$777$		0			0
$778$	2.70418	+	12.9472i	0.0969497	+	0.464181i
$779$	−7.39361	+	12.8061i	−0.264903	+	0.458826i
$780$	−5.92473	−	24.1735i	−0.212139	−	0.865549i
$781$	−3.62174	−	6.27304i	−0.129596	−	0.224467i
$782$	−1.95446	−	0.642695i	−0.0698913	−	0.0229827i
$783$	−28.3379	+	28.3379i	−1.01271	+	1.01271i
$784$		0			0
$785$	−16.7650	+	1.51885i	−0.598367	+	0.0542102i
$786$	2.05297	−	1.03691i	0.0732269	−	0.0369852i
$787$	0.279451	−	1.04293i	0.00996136	−	0.0371763i	−0.960766	−	0.277359i	$-0.910541\pi$
$787$	0.279451	−	1.04293i	0.00996136	−	0.0371763i	0.970728	+	0.240183i	$0.0772074\pi$
$788$	−46.1224	+	6.97092i	−1.64304	+	0.248329i
$789$	−11.4095	−	6.58729i	−0.406189	−	0.234514i
$790$	−29.8610	−	15.8947i	−1.06240	−	0.565510i
$791$		0			0
$792$	−3.17471	+	2.25547i	−0.112808	+	0.0801447i
$793$	−25.9757	+	6.96017i	−0.922424	+	0.247163i
$794$	25.0908	+	1.40398i	0.890439	+	0.0498253i
$795$	−1.39790	+	8.07338i	−0.0495783	+	0.286333i
$796$	2.15447	−	19.1912i	0.0763630	−	0.680213i
$797$	13.9414	−	13.9414i	0.493829	−	0.493829i	−0.415681	−	0.909510i	$-0.636457\pi$
$797$	13.9414	−	13.9414i	0.493829	−	0.493829i	0.909510	+	0.415681i	$0.136457\pi$
$798$		0			0
$799$	−8.52950			−0.301752
$800$	21.8750	−	17.9299i	0.773399	−	0.633919i
$801$	−1.53111	−	2.65196i	−0.0540992	−	0.0937025i
$802$	5.80002	+	6.48759i	0.204806	+	0.229085i
$803$	−3.62754	−	13.5382i	−0.128013	−	0.477751i
$804$	34.0401	−	14.8679i	1.20050	−	0.524352i
$805$		0			0
$806$	13.6479	−	20.8540i	0.480726	−	0.734550i
$807$	−14.6862	+	3.93515i	−0.516978	+	0.138524i
$808$	3.67768	+	1.68440i	0.129380	+	0.0592571i
$809$	−4.37439	+	2.52555i	−0.153795	+	0.0887937i	−0.574923	−	0.818208i	$-0.694968\pi$
$809$	−4.37439	+	2.52555i	−0.153795	+	0.0887937i	0.421127	+	0.907001i	$0.361635\pi$
$810$	6.89736	−	4.30559i	0.242348	−	0.151283i
$811$			21.1629i			0.743131i	0.928407	+	0.371565i	$0.121179\pi$
$811$			21.1629i			0.743131i	−0.928407	+	0.371565i	$0.878821\pi$
$812$		0			0
$813$	−5.80185	−	5.80185i	−0.203480	−	0.203480i
$814$	−1.25012	+	0.631405i	−0.0438165	+	0.0221307i
$815$	−8.56522	−	12.1525i	−0.300027	−	0.425682i
$816$	−2.94044	+	12.9311i	−0.102936	+	0.452680i
$817$	−12.7255	−	47.4920i	−0.445207	−	1.66154i
$818$	1.89274	+	9.06216i	0.0661781	+	0.316851i
$819$		0			0
$820$	−15.9498	−	4.64251i	−0.556991	−	0.162124i
$821$	−21.3620	+	37.0001i	−0.745540	+	1.29131i	0.204402	+	0.978887i	$0.434475\pi$
$821$	−21.3620	+	37.0001i	−0.745540	+	1.29131i	−0.949942	+	0.312426i	$0.898858\pi$
$822$	1.52445	−	1.36289i	0.0531714	−	0.0475362i
$823$	4.61152	+	1.23565i	0.160748	+	0.0430722i	0.338295	−	0.941040i	$-0.390150\pi$
$823$	4.61152	+	1.23565i	0.160748	+	0.0430722i	−0.177548	+	0.984112i	$0.556816\pi$
$824$	−22.1736	−	18.3489i	−0.772456	−	0.639215i
$825$	3.37417	−	4.88263i	0.117474	−	0.169992i
$826$		0			0
$827$	−6.21884	−	6.21884i	−0.216250	−	0.216250i	0.590666	−	0.806916i	$-0.298865\pi$
$827$	−6.21884	−	6.21884i	−0.216250	−	0.216250i	−0.806916	+	0.590666i	$0.798865\pi$
$828$	−1.23645	+	0.986854i	−0.0429696	+	0.0342956i
$829$	−33.7077	+	19.4612i	−1.17072	+	0.675915i	−0.953849	−	0.300286i	$-0.902918\pi$
$829$	−33.7077	+	19.4612i	−1.17072	+	0.675915i	−0.216869	+	0.976201i	$0.569585\pi$
$830$	18.7151	+	17.4681i	0.649612	+	0.606325i
$831$	−4.43367	−	2.55978i	−0.153802	−	0.0887978i
$832$	32.1594	−	15.5353i	1.11493	−	0.538588i
$833$		0			0
$834$	16.8475	−	25.7431i	0.583383	−	0.891410i
$835$	17.0271	+	7.87605i	0.589248	+	0.272562i
$836$	4.49947	−	6.10173i	0.155617	−	0.211033i
$837$	21.1330	+	5.66257i	0.730464	+	0.195727i
$838$	−7.85948	+	23.9009i	−0.271501	+	0.825645i
$839$	15.0742			0.520418			0.260209	−	0.965552i	$-0.416209\pi$
$839$	15.0742			0.520418			0.260209	+	0.965552i	$0.416209\pi$
$840$		0			0
$841$	−23.2844			−0.802910
$842$	−7.27500	+	22.1235i	−0.250713	+	0.762427i
$843$	38.8660	+	10.4141i	1.33862	+	0.358681i
$844$	−12.3855	+	16.7960i	−0.426327	+	0.578141i
$845$	−5.34545	−	14.5468i	−0.183889	−	0.500424i
$846$	−3.59146	+	5.48776i	−0.123477	+	0.188673i
$847$		0			0
$848$	−11.7489	+	0.449132i	−0.403461	+	0.0154233i
$849$	−21.0823	−	12.1719i	−0.723543	−	0.417738i
$850$	2.34087	+	18.6590i	0.0802910	+	0.640000i
$851$	−0.492709	+	0.284465i	−0.0168898	+	0.00975135i
$852$	−14.8235	+	11.8312i	−0.507845	+	0.405329i
$853$	14.0097	+	14.0097i	0.479684	+	0.479684i	0.905031	−	0.425346i	$-0.139848\pi$
$853$	14.0097	+	14.0097i	0.479684	+	0.479684i	−0.425346	+	0.905031i	$0.639848\pi$
$854$		0			0
$855$	8.24327	−	9.88570i	0.281914	−	0.338084i
$856$	−0.0725349	+	0.0876544i	−0.00247919	+	0.00299597i
$857$	−34.4324	−	9.22615i	−1.17619	−	0.315159i	−0.382776	−	0.923841i	$-0.625032\pi$
$857$	−34.4324	−	9.22615i	−1.17619	−	0.315159i	−0.793414	+	0.608682i	$0.791698\pi$
$858$	5.58710	−	4.99497i	0.190740	−	0.170525i
$859$	−26.2004	+	45.3805i	−0.893947	+	1.54836i	−0.0588442	+	0.998267i	$0.518742\pi$
$859$	−26.2004	+	45.3805i	−0.893947	+	1.54836i	−0.835103	+	0.550094i	$0.814592\pi$
$860$	48.4151	−	26.5848i	1.65094	−	0.906536i
$861$		0			0
$862$	−4.37546	−	20.9491i	−0.149029	−	0.713528i
$863$	−1.36585	−	5.09743i	−0.0464941	−	0.173518i	0.938775	−	0.344532i	$-0.111962\pi$
$863$	−1.36585	−	5.09743i	−0.0464941	−	0.173518i	−0.985269	+	0.171014i	$0.945296\pi$
$864$	21.7739	+	22.5582i	0.740763	+	0.767444i
$865$	4.04584	−	2.85156i	0.137563	−	0.0969559i
$866$	9.73623	−	4.91755i	0.330851	−	0.167105i
$867$	8.75067	+	8.75067i	0.297188	+	0.297188i
$868$		0			0
$869$		−	10.1859i		−	0.345535i
$870$	27.7711	+	6.42475i	0.941529	+	0.217819i
$871$	57.6023	−	33.2567i	1.95178	−	1.12686i
$872$	−7.41169	+	16.1825i	−0.250992	+	0.548009i
$873$	−6.09536	+	1.63325i	−0.206297	+	0.0552771i
$874$	1.68647	−	2.57694i	0.0570458	−	0.0871662i
$875$		0			0
$876$	−33.6304	+	14.6890i	−1.13627	+	0.496295i
$877$	−2.89005	−	10.7858i	−0.0975901	−	0.364211i	0.899809	−	0.436283i	$-0.143705\pi$
$877$	−2.89005	−	10.7858i	−0.0975901	−	0.364211i	−0.997399	+	0.0720722i	$0.977039\pi$
$878$	−24.2677	−	27.1445i	−0.818995	−	0.916083i
$879$	11.1824	+	19.3685i	0.377174	+	0.653285i
$880$	7.86078	+	3.27762i	0.264987	+	0.110488i
$881$	−22.0701			−0.743561			−0.371781	−	0.928321i	$-0.621253\pi$
$881$	−22.0701			−0.743561			−0.371781	+	0.928321i	$0.621253\pi$
$882$		0			0
$883$	5.32169	−	5.32169i	0.179089	−	0.179089i	−0.611869	−	0.790959i	$-0.709582\pi$
$883$	5.32169	−	5.32169i	0.179089	−	0.179089i	0.790959	+	0.611869i	$0.209582\pi$
$884$	−2.64915	+	23.5976i	−0.0891005	+	0.793674i
$885$	20.2367	+	28.7122i	0.680250	+	0.965149i
$886$	−24.4127	−	1.36603i	−0.820159	−	0.0458928i
$887$	4.89193	−	1.31079i	0.164255	−	0.0440120i	−0.175754	−	0.984434i	$-0.556236\pi$
$887$	4.89193	−	1.31079i	0.164255	−	0.0440120i	0.340009	+	0.940422i	$0.389570\pi$
$888$	2.12385	+	2.98944i	0.0712718	+	0.100319i
$889$		0			0
$890$	−3.14670	+	5.91161i	−0.105478	+	0.198157i
$891$	2.12030	+	1.22416i	0.0710327	+	0.0410108i
$892$	−29.9976	+	4.53382i	−1.00439	+	0.151803i
$893$	3.30454	−	12.3327i	0.110582	−	0.412699i
$894$	−17.6419	+	8.91052i	−0.590033	+	0.298012i
$895$	−28.2845	−	23.5853i	−0.945448	−	0.788369i
$896$		0			0
$897$	2.15273	−	2.15273i	0.0718774	−	0.0718774i
$898$	14.9121	+	4.90364i	0.497625	+	0.163637i
$899$	14.2718	+	24.7194i	0.475990	+	0.824439i
$900$	12.9906	+	6.35054i	0.433020	+	0.211685i
$901$	3.90860	−	6.76989i	0.130214	−	0.225538i
$902$	−1.02265	−	4.89633i	−0.0340507	−	0.163030i
$903$		0			0
$904$	−42.7964	−	7.24469i	−1.42339	−	0.240955i
$905$	−12.5435	+	4.60930i	−0.416959	+	0.153218i
$906$	1.47943	−	26.4392i	0.0491507	−	0.878382i
$907$	0.876735	−	3.27202i	0.0291115	−	0.108646i	−0.949841	−	0.312732i	$-0.898756\pi$
$907$	0.876735	−	3.27202i	0.0291115	−	0.108646i	0.978953	+	0.204087i	$0.0654224\pi$
$908$	15.6665	−	12.5040i	0.519911	−	0.414959i
$909$			2.06796i			0.0685899i
$910$		0			0
$911$		−	31.5983i		−	1.04690i	−0.852057	−	0.523449i	$-0.824645\pi$
$911$		−	31.5983i		−	1.04690i	0.852057	−	0.523449i	$-0.175355\pi$
$912$	−17.5578	−	9.26140i	−0.581397	−	0.306676i
$913$	−1.99514	+	7.44597i	−0.0660295	+	0.246426i
$914$	−29.9877	−	1.67799i	−0.991905	−	0.0555030i
$915$	−7.04919	+	15.2396i	−0.233039	+	0.503804i
$916$	−13.6796	−	31.3195i	−0.451988	−	1.03482i
$917$		0			0
$918$	−20.4049	+	4.26180i	−0.673462	+	0.140660i
$919$	−23.1351	+	40.0712i	−0.763157	+	1.32183i	0.178058	+	0.984020i	$0.443018\pi$
$919$	−23.1351	+	40.0712i	−0.763157	+	1.32183i	−0.941215	+	0.337807i	$0.890315\pi$
$920$	3.26267	+	1.15098i	0.107567	+	0.0379466i
$921$	8.79800	+	15.2386i	0.289904	+	0.502128i
$922$	3.80653	−	11.5758i	0.125362	−	0.381229i
$923$	−24.0141	+	24.0141i	−0.790435	+	0.790435i
$924$		0			0
$925$	4.27804	+	2.95637i	0.140661	+	0.0972047i
$926$	−1.47279	−	2.91596i	−0.0483987	−	0.0958244i
$927$	3.80821	−	14.2124i	0.125078	−	0.466797i
$928$	−0.723497	+	40.8972i	−0.0237499	+	1.34251i
$929$	−37.0594	−	21.3962i	−1.21588	−	0.701987i	−0.251844	−	0.967768i	$-0.581037\pi$
$929$	−37.0594	−	21.3962i	−1.21588	−	0.701987i	−0.964034	+	0.265780i	$0.914370\pi$
$930$	−4.54297	−	14.8836i	−0.148970	−	0.488051i
$931$		0			0
$932$	−3.49220	−	1.36896i	−0.114391	−	0.0448418i
$933$	16.7837	−	4.49719i	0.549475	−	0.147231i
$934$	2.01323	−	35.9789i	0.0658750	−	1.17727i
$935$	−4.62841	+	3.26216i	−0.151365	+	0.106684i
$936$	14.0669	+	11.6405i	0.459791	+	0.380482i
$937$	−18.9957	+	18.9957i	−0.620561	+	0.620561i	−0.945675	−	0.325114i	$-0.894597\pi$
$937$	−18.9957	+	18.9957i	−0.620561	+	0.620561i	0.325114	+	0.945675i	$0.394597\pi$
$938$		0			0
$939$	−6.11875			−0.199678
$940$	14.3398	+	0.307566i	0.467713	+	0.0100317i
$941$	−10.8404	−	18.7762i	−0.353388	−	0.612086i	0.633453	−	0.773781i	$-0.281637\pi$
$941$	−10.8404	−	18.7762i	−0.353388	−	0.612086i	−0.986841	+	0.161696i	$0.948304\pi$
$942$	−9.89437	+	8.84575i	−0.322376	+	0.288210i
$943$	−0.525906	−	1.96271i	−0.0171258	−	0.0639145i
$944$	−34.2554	+	36.9785i	−1.11492	+	1.20355i
$945$		0			0
$946$	13.9163	+	9.10749i	0.452457	+	0.296110i
$947$	14.8363	−	3.97536i	0.482114	−	0.129182i	−0.00957300	−	0.999954i	$-0.503047\pi$
$947$	14.8363	−	3.97536i	0.482114	−	0.129182i	0.491687	+	0.870772i	$0.336381\pi$
$948$	−26.3711	+	3.98571i	−0.856493	+	0.129450i
$949$	−56.9090	+	32.8564i	−1.84735	+	1.06657i
$950$	−27.8858	−	3.84435i	−0.904736	−	0.124727i
$951$		−	42.8869i		−	1.39070i
$952$		0			0
$953$	22.0087	+	22.0087i	0.712931	+	0.712931i	0.967147	−	0.254216i	$-0.0818174\pi$
$953$	22.0087	+	22.0087i	0.712931	+	0.712931i	−0.254216	+	0.967147i	$0.581817\pi$
$954$	−2.70988	−	5.36528i	−0.0877357	−	0.173708i
$955$	−17.7283	−	3.06964i	−0.573674	−	0.0993311i
$956$	24.4964	+	18.0639i	0.792271	+	0.584228i
$957$	2.22146	+	8.29061i	0.0718096	+	0.267997i
$958$	−12.8446	+	2.68274i	−0.414990	+	0.0866755i
$959$		0			0
$960$	5.40976	−	21.6338i	0.174599	−	0.698228i
$961$	−7.70864	+	13.3518i	−0.248666	+	0.430702i
$962$	4.37647	+	4.89527i	0.141103	+	0.157830i
$963$	−0.0561830	−	0.0150542i	−0.00181047	−	0.000485114i
$964$	−2.93981	+	26.1867i	−0.0946848	+	0.843417i
$965$	−2.93747	−	32.4235i	−0.0945604	−	1.04375i
$966$		0			0
$967$	16.9281	+	16.9281i	0.544372	+	0.544372i	0.924807	−	0.380435i	$-0.124226\pi$
$967$	16.9281	+	16.9281i	0.544372	+	0.544372i	−0.380435	+	0.924807i	$0.624226\pi$
$968$	−2.68261	−	28.4219i	−0.0862223	−	0.913514i
$969$	11.4299	−	6.59904i	0.367180	−	0.211992i
$970$	10.0888	+	9.41649i	0.323931	+	0.302345i
$971$	−32.1198	−	18.5444i	−1.03077	−	0.595118i	−0.113568	−	0.993530i	$-0.536228\pi$
$971$	−32.1198	−	18.5444i	−1.03077	−	0.595118i	−0.917206	+	0.398412i	$0.869561\pi$
$972$	−9.79698	+	24.9920i	−0.314238	+	0.801620i
$973$		0			0
$974$	−21.0739	−	13.7918i	−0.675251	−	0.441918i
$975$	−26.2067	−	9.35584i	−0.839287	−	0.299627i
$976$	−23.4949	−	5.34256i	−0.752053	−	0.171011i
$977$	−22.5762	−	6.04928i	−0.722277	−	0.193534i	−0.121090	−	0.992642i	$-0.538639\pi$
$977$	−22.5762	−	6.04928i	−0.722277	−	0.193534i	−0.601188	+	0.799108i	$0.705306\pi$
$978$	−11.1353	−	3.66170i	−0.356069	−	0.117088i
$979$	−2.01652			−0.0644484
$980$		0			0
$981$	−9.09942			−0.290522
$982$	−3.35820	−	1.10430i	−0.107165	−	0.0352395i
$983$	19.2069	+	5.14648i	0.612606	+	0.164147i	0.551764	−	0.834000i	$-0.313955\pi$
$983$	19.2069	+	5.14648i	0.612606	+	0.164147i	0.0608417	+	0.998147i	$0.480622\pi$
$984$	−12.2763	+	4.56353i	−0.391353	+	0.145480i
$985$	−21.8946	+	47.3336i	−0.697619	+	1.50817i
$986$	−22.7555	−	14.8923i	−0.724682	−	0.474268i
$987$		0			0
$988$	−33.0932	−	12.9727i	−1.05284	−	0.412716i
$989$	5.85104	+	3.37810i	0.186052	+	0.107417i
$990$	0.149977	+	4.35142i	0.00476658	+	0.138297i
$991$	19.5362	−	11.2792i	0.620586	−	0.358296i	−0.156511	−	0.987676i	$-0.550025\pi$
$991$	19.5362	−	11.2792i	0.620586	−	0.358296i	0.777097	+	0.629380i	$0.216691\pi$
$992$	19.5332	−	10.8214i	0.620178	−	0.343580i
$993$	11.4204	+	11.4204i	0.362414	+	0.362414i
$994$		0			0
$995$	−16.5825	−	13.8275i	−0.525701	−	0.438360i
$996$	20.0581	+	2.25178i	0.635564	+	0.0713505i
$997$	16.6372	+	4.45792i	0.526905	+	0.141184i	0.512459	−	0.858712i	$-0.328735\pi$
$997$	16.6372	+	4.45792i	0.526905	+	0.141184i	0.0144466	+	0.999896i	$0.495401\pi$
$998$	−6.14930	−	6.87827i	−0.194653	−	0.217728i
$999$	−2.88213	+	4.99199i	−0.0911865	+	0.157940i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.x.m.863.11		72
4.3	odd	2	inner	980.2.x.m.863.5		72
5.2	odd	4	inner	980.2.x.m.667.17		72
7.2	even	3		980.2.k.j.883.1		36
7.3	odd	6		140.2.w.b.123.14	yes	72
7.4	even	3	inner	980.2.x.m.263.14		72
7.5	odd	6		980.2.k.k.883.1		36
7.6	odd	2		140.2.w.b.23.11	yes	72
20.7	even	4	inner	980.2.x.m.667.14		72
28.3	even	6		140.2.w.b.123.17	yes	72
28.11	odd	6	inner	980.2.x.m.263.17		72
28.19	even	6		980.2.k.k.883.8		36
28.23	odd	6		980.2.k.j.883.8		36
28.27	even	2		140.2.w.b.23.5	✓	72
35.2	odd	12		980.2.k.j.687.8		36
35.3	even	12		700.2.be.e.207.14		72
35.12	even	12		980.2.k.k.687.8		36
35.13	even	4		700.2.be.e.107.2		72
35.17	even	12		140.2.w.b.67.5	yes	72
35.24	odd	6		700.2.be.e.543.5		72
35.27	even	4		140.2.w.b.107.17	yes	72
35.32	odd	12	inner	980.2.x.m.67.5		72
35.34	odd	2		700.2.be.e.443.8		72
140.3	odd	12		700.2.be.e.207.8		72
140.27	odd	4		140.2.w.b.107.14	yes	72
140.47	odd	12		980.2.k.k.687.1		36
140.59	even	6		700.2.be.e.543.2		72
140.67	even	12	inner	980.2.x.m.67.11		72
140.83	odd	4		700.2.be.e.107.5		72
140.87	odd	12		140.2.w.b.67.11	yes	72
140.107	even	12		980.2.k.j.687.1		36
140.139	even	2		700.2.be.e.443.14		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.w.b.23.5	✓	72	28.27	even	2
140.2.w.b.23.11	yes	72	7.6	odd	2
140.2.w.b.67.5	yes	72	35.17	even	12
140.2.w.b.67.11	yes	72	140.87	odd	12
140.2.w.b.107.14	yes	72	140.27	odd	4
140.2.w.b.107.17	yes	72	35.27	even	4
140.2.w.b.123.14	yes	72	7.3	odd	6
140.2.w.b.123.17	yes	72	28.3	even	6
700.2.be.e.107.2		72	35.13	even	4
700.2.be.e.107.5		72	140.83	odd	4
700.2.be.e.207.8		72	140.3	odd	12
700.2.be.e.207.14		72	35.3	even	12
700.2.be.e.443.8		72	35.34	odd	2
700.2.be.e.443.14		72	140.139	even	2
700.2.be.e.543.2		72	140.59	even	6
700.2.be.e.543.5		72	35.24	odd	6
980.2.k.j.687.1		36	140.107	even	12
980.2.k.j.687.8		36	35.2	odd	12
980.2.k.j.883.1		36	7.2	even	3
980.2.k.j.883.8		36	28.23	odd	6
980.2.k.k.687.1		36	140.47	odd	12
980.2.k.k.687.8		36	35.12	even	12
980.2.k.k.883.1		36	7.5	odd	6
980.2.k.k.883.8		36	28.19	even	6
980.2.x.m.67.5		72	35.32	odd	12	inner
980.2.x.m.67.11		72	140.67	even	12	inner
980.2.x.m.263.14		72	7.4	even	3	inner
980.2.x.m.263.17		72	28.11	odd	6	inner
980.2.x.m.667.14		72	20.7	even	4	inner
980.2.x.m.667.17		72	5.2	odd	4	inner
980.2.x.m.863.5		72	4.3	odd	2	inner
980.2.x.m.863.11		72	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.441772 - 1.34344i) q^{2} +(-1.20413 - 0.322645i) q^{3} +(-1.60968 - 1.18699i) q^{4} +(-2.09885 + 0.771256i) q^{5} +(-0.965404 + 1.47514i) q^{6} +(-2.30576 + 1.63813i) q^{8} +(-1.25225 - 0.722989i) q^{9} +(0.108927 + 3.16040i) q^{10} +(-0.824629 + 0.476100i) q^{11} +(1.55528 + 1.94864i) q^{12} +(3.15680 + 3.15680i) q^{13} +(2.77612 - 0.251508i) q^{15} +(1.18211 + 3.82134i) q^{16} +(-2.56885 - 0.688322i) q^{17} +(-1.52450 + 1.36293i) q^{18} +(1.99048 - 3.44760i) q^{19} +(4.29394 + 1.24984i) q^{20} +(0.275315 + 1.31817i) q^{22} +(0.141582 + 0.528392i) q^{23} +(3.30496 - 1.22857i) q^{24} +(3.81033 - 3.23750i) q^{25} +(5.63557 - 2.84640i) q^{26} +(3.91905 + 3.91905i) q^{27} +7.23080i q^{29} +(0.888526 - 3.84067i) q^{30} +(3.41863 - 1.97375i) q^{31} +(5.65597 + 0.100058i) q^{32} +(1.14657 - 0.307222i) q^{33} +(-2.05957 + 3.14702i) q^{34} +(1.15754 + 2.65019i) q^{36} +(0.269180 + 1.00460i) q^{37} +(-3.75232 - 4.19714i) q^{38} +(-2.78267 - 4.81972i) q^{39} +(3.57603 - 5.21652i) q^{40} -3.71449 q^{41} +(8.73324 - 8.73324i) q^{43} +(1.89251 + 0.212459i) q^{44} +(3.18590 + 0.551635i) q^{45} +(0.772411 + 0.0432210i) q^{46} +(3.09794 - 0.830089i) q^{47} +(-0.190479 - 4.98278i) q^{48} +(-2.66610 - 6.54919i) q^{50} +(2.87114 + 1.65765i) q^{51} +(-1.33434 - 8.82853i) q^{52} +(-0.760768 + 2.83923i) q^{53} +(6.99635 - 3.53369i) q^{54} +(1.36358 - 1.63526i) q^{55} +(-3.50914 + 3.50914i) q^{57} +(9.71416 + 3.19436i) q^{58} +(6.30084 + 10.9134i) q^{59} +(-4.76720 - 2.89038i) q^{60} +(-3.01183 + 5.21665i) q^{61} +(-1.14136 - 5.46468i) q^{62} +(2.63307 - 7.55427i) q^{64} +(-9.06036 - 4.19095i) q^{65} +(0.0937861 - 1.67607i) q^{66} +(3.85605 - 14.3910i) q^{67} +(3.31799 + 4.15717i) q^{68} -0.681932i q^{69} +7.60710i q^{71} +(4.07174 - 0.384313i) q^{72} +(-3.80964 + 14.2178i) q^{73} +(1.46853 + 0.0821731i) q^{74} +(-5.63268 + 2.66898i) q^{75} +(-7.29629 + 3.18685i) q^{76} +(-7.70432 + 1.60914i) q^{78} +(-5.34864 + 9.26412i) q^{79} +(-5.42830 - 7.10869i) q^{80} +(-1.28561 - 2.22674i) q^{81} +(-1.64096 + 4.99021i) q^{82} +(5.72446 - 5.72446i) q^{83} +(5.92250 - 0.536560i) q^{85} +(-7.87451 - 15.5907i) q^{86} +(2.33298 - 8.70680i) q^{87} +(1.12148 - 2.44862i) q^{88} +(1.83403 + 1.05888i) q^{89} +(2.14853 - 4.03637i) q^{90} +(0.399294 - 1.01860i) q^{92} +(-4.75329 + 1.27364i) q^{93} +(0.253402 - 4.52861i) q^{94} +(-1.51872 + 8.77117i) q^{95} +(-6.77823 - 1.94535i) q^{96} +(3.08588 - 3.08588i) q^{97} +1.37686 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 2 q^{2} + 8 q^{5} + 16 q^{6} - 4 q^{8} - 2 q^{10} - 10 q^{12} - 28 q^{16} - 4 q^{17} - 20 q^{18} + 56 q^{20} - 16 q^{22} - 16 q^{25} + 4 q^{26} - 32 q^{30} - 38 q^{32} + 64 q^{33} + 16 q^{36} - 4 q^{37}+ \cdots + 24 q^{97}+O(q^{100}) \) 72 * q + 2 * q^2 + 8 * q^5 + 16 * q^6 - 4 * q^8 - 2 * q^10 - 10 * q^12 - 28 * q^16 - 4 * q^17 - 20 * q^18 + 56 * q^20 - 16 * q^22 - 16 * q^25 + 4 * q^26 - 32 * q^30 - 38 * q^32 + 64 * q^33 + 16 * q^36 - 4 * q^37 - 12 * q^38 - 2 * q^40 + 40 * q^41 + 12 * q^45 - 28 * q^46 - 12 * q^48 - 28 * q^50 - 48 * q^52 - 24 * q^53 - 16 * q^57 + 30 * q^58 - 10 * q^60 + 20 * q^61 - 56 * q^62 + 4 * q^65 - 44 * q^66 + 12 * q^68 + 44 * q^72 + 12 * q^73 - 112 * q^76 + 64 * q^78 - 52 * q^80 - 52 * q^81 + 34 * q^82 + 16 * q^85 + 64 * q^86 + 16 * q^88 + 32 * q^90 + 44 * q^92 + 12 * q^93 + 48 * q^96 + 24 * q^97

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